CINXE.COM

<!doctype html><html lang=de><head><meta charset=utf-8> <script>var __ezHttpConsent={setByCat:function(src,tagType,attributes,category,force){var setScript=function(){if(force||window.ezTcfConsent[category]){var scriptElement=document.createElement(tagType);scriptElement.src=src;attributes.forEach(function(attr){for(var key in attr){if(attr.hasOwnProperty(key)){scriptElement.setAttribute(key,attr[key]);}}});var firstScript=document.getElementsByTagName(tagType)[0];firstScript.parentNode.insertBefore(scriptElement,firstScript);}};if(force||(window.ezTcfConsent&&window.ezTcfConsent.loaded)){setScript();}else if(typeof getEzConsentData==="function"){getEzConsentData().then(function(ezTcfConsent){if(ezTcfConsent&&ezTcfConsent.loaded){setScript();}else{console.error("cannot get ez consent data");force=true;setScript();}});}else{force=true;setScript();console.error("getEzConsentData is not a function");}},};</script> <script>var ezTcfConsent=window.ezTcfConsent?window.ezTcfConsent:{loaded:false,store_info:false,develop_and_improve_services:false,measure_ad_performance:false,measure_content_performance:false,select_basic_ads:false,create_ad_profile:false,select_personalized_ads:false,create_content_profile:false,select_personalized_content:false,understand_audiences:false,use_limited_data_to_select_content:false,};function getEzConsentData(){return new Promise(function(resolve){document.addEventListener("ezConsentEvent",function(event){var ezTcfConsent=event.detail.ezTcfConsent;resolve(ezTcfConsent);});});}</script> <script>if(typeof _setEzCookies!=='function'){function _setEzCookies(ezConsentData){var cookies=window.ezCookieQueue;for(var i=0;i<cookies.length;i++){var cookie=cookies[i];if(ezConsentData&&ezConsentData.loaded&&ezConsentData[cookie.tcfCategory]){document.cookie=cookie.name+"="+cookie.value;}}}} window.ezCookieQueue=window.ezCookieQueue||[];if(typeof addEzCookies!=='function'){function addEzCookies(arr){window.ezCookieQueue=[...window.ezCookieQueue,...arr];}} addEzCookies([{name:"ezoab_140745",value:"mod30; Path=/; Domain=123mathe.de; Max-Age=7200",tcfCategory:"store_info",isEzoic:"true",},{name:"ezosuibasgeneris-1",value:"f047a942-dacd-4b24-4f11-6717f21ca75e; Path=/; Domain=123mathe.de; Expires=Fri, 20 Feb 2026 01:14:50 UTC; Secure; SameSite=None",tcfCategory:"understand_audiences",isEzoic:"true",}]);if(window.ezTcfConsent&&window.ezTcfConsent.loaded){_setEzCookies(window.ezTcfConsent);}else if(typeof getEzConsentData==="function"){getEzConsentData().then(function(ezTcfConsent){if(ezTcfConsent&&ezTcfConsent.loaded){_setEzCookies(window.ezTcfConsent);}else{console.error("cannot get ez consent data");_setEzCookies(window.ezTcfConsent);}});}else{console.error("getEzConsentData is not a function");_setEzCookies(window.ezTcfConsent);}</script><script type="text/javascript" data-ezscrex='false' data-cfasync='false'>window._ezaq = Object.assign({"edge_cache_status":12,"edge_response_time":904,"url":"https://123mathe.de/mengenbegriff"}, typeof window._ezaq !== "undefined" ? window._ezaq : {});</script><script type="text/javascript" data-ezscrex='false' data-cfasync='false'>window._ezaq = Object.assign({"ab_test_id":"mod30"}, typeof window._ezaq !== "undefined" ? window._ezaq : {});window.__ez=window.__ez||{};window.__ez.tf={};</script><script type="text/javascript" data-ezscrex='false' data-cfasync='false'>window.ezDisableAds = true;</script><script data-ezscrex=false data-cfasync=false data-pagespeed-no-defer>var __ez=__ez||{};__ez.stms=Date.now();__ez.evt={};__ez.script={};__ez.ck=__ez.ck||{};__ez.template={};__ez.template.isOrig=true;window.__ezScriptHost="//www.ezojs.com";__ez.queue=__ez.queue||function(){var e=0,i=0,t=[],n=!1,o=[],r=[],s=!0,a=function(e,i,n,o,r,s,a){var l=arguments.length>7&&void 0!==arguments[7]?arguments[7]:window,d=this;this.name=e,this.funcName=i,this.parameters=null===n?null:w(n)?n:[n],this.isBlock=o,this.blockedBy=r,this.deleteWhenComplete=s,this.isError=!1,this.isComplete=!1,this.isInitialized=!1,this.proceedIfError=a,this.fWindow=l,this.isTimeDelay=!1,this.process=function(){f("... func = "+e),d.isInitialized=!0,d.isComplete=!0,f("... func.apply: "+e);var i=d.funcName.split("."),n=null,o=this.fWindow||window;i.length>3||(n=3===i.length?o[i[0]][i[1]][i[2]]:2===i.length?o[i[0]][i[1]]:o[d.funcName]),null!=n&&n.apply(null,this.parameters),!0===d.deleteWhenComplete&&delete t[e],!0===d.isBlock&&(f("----- F'D: "+d.name),m())}},l=function(e,i,t,n,o,r,s){var a=arguments.length>7&&void 0!==arguments[7]?arguments[7]:window,l=this;this.name=e,this.path=i,this.async=o,this.defer=r,this.isBlock=t,this.blockedBy=n,this.isInitialized=!1,this.isError=!1,this.isComplete=!1,this.proceedIfError=s,this.fWindow=a,this.isTimeDelay=!1,this.isPath=function(e){return"/"===e[0]&&"/"!==e[1]},this.getSrc=function(e){return void 0!==window.__ezScriptHost&&this.isPath(e)&&"banger.js"!==this.name?window.__ezScriptHost+e:e},this.process=function(){l.isInitialized=!0,f("... file = "+e);var i=this.fWindow?this.fWindow.document:document,t=i.createElement("script");t.src=this.getSrc(this.path),!0===o?t.async=!0:!0===r&&(t.defer=!0),t.onerror=function(){var e={url:window.location.href,name:l.name,path:l.path,user_agent:window.navigator.userAgent};"undefined"!=typeof _ezaq&&(e.pageview_id=_ezaq.page_view_id);var i=encodeURIComponent(JSON.stringify(e)),t=new XMLHttpRequest;t.open("GET","//g.ezoic.net/ezqlog?d="+i,!0),t.send(),f("----- ERR'D: "+l.name),l.isError=!0,!0===l.isBlock&&m()},t.onreadystatechange=t.onload=function(){var e=t.readyState;f("----- F'D: "+l.name),e&&!/loaded|complete/.test(e)||(l.isComplete=!0,!0===l.isBlock&&m())},i.getElementsByTagName("head")[0].appendChild(t)}},d=function(e,i){this.name=e,this.path="",this.async=!1,this.defer=!1,this.isBlock=!1,this.blockedBy=[],this.isInitialized=!0,this.isError=!1,this.isComplete=i,this.proceedIfError=!1,this.isTimeDelay=!1,this.process=function(){}};function c(e,i,n,s,a,d,c,u,f){var m=new l(e,i,n,s,a,d,c,f);!0===u?o[e]=m:r[e]=m,t[e]=m,h(m)}function h(e){!0!==u(e)&&0!=s&&e.process()}function u(e){if(!0===e.isTimeDelay&&!1===n)return f(e.name+" blocked = TIME DELAY!"),!0;if(w(e.blockedBy))for(var i=0;i<e.blockedBy.length;i++){var o=e.blockedBy[i];if(!1===t.hasOwnProperty(o))return f(e.name+" blocked = "+o),!0;if(!0===e.proceedIfError&&!0===t[o].isError)return!1;if(!1===t[o].isComplete)return f(e.name+" blocked = "+o),!0}return!1}function f(e){var i=window.location.href,t=new RegExp("[?&]ezq=([^&#]*)","i").exec(i);"1"===(t?t[1]:null)&&console.debug(e)}function m(){++e>200||(f("let's go"),p(o),p(r))}function p(e){for(var i in e)if(!1!==e.hasOwnProperty(i)){var t=e[i];!0===t.isComplete||u(t)||!0===t.isInitialized||!0===t.isError?!0===t.isError?f(t.name+": error"):!0===t.isComplete?f(t.name+": complete already"):!0===t.isInitialized&&f(t.name+": initialized already"):t.process()}}function w(e){return"[object Array]"==Object.prototype.toString.call(e)}return window.addEventListener("load",(function(){setTimeout((function(){n=!0,f("TDELAY -----"),m()}),5e3)}),!1),{addFile:c,addFileOnce:function(e,i,n,o,r,s,a,l,d){t[e]||c(e,i,n,o,r,s,a,l,d)},addDelayFile:function(e,i){var n=new l(e,i,!1,[],!1,!1,!0);n.isTimeDelay=!0,f(e+" ... FILE! TDELAY"),r[e]=n,t[e]=n,h(n)},addFunc:function(e,n,s,l,d,c,u,f,m,p){!0===c&&(e=e+"_"+i++);var w=new a(e,n,s,l,d,u,f,p);!0===m?o[e]=w:r[e]=w,t[e]=w,h(w)},addDelayFunc:function(e,i,n){var o=new a(e,i,n,!1,[],!0,!0);o.isTimeDelay=!0,f(e+" ... FUNCTION! TDELAY"),r[e]=o,t[e]=o,h(o)},items:t,processAll:m,setallowLoad:function(e){s=e},markLoaded:function(e){if(e&&0!==e.length){if(e in t){var i=t[e];!0===i.isComplete?f(i.name+" "+e+": error loaded duplicate"):(i.isComplete=!0,i.isInitialized=!0)}else t[e]=new d(e,!0);f("markLoaded dummyfile: "+t[e].name)}},logWhatsBlocked:function(){for(var e in t)!1!==t.hasOwnProperty(e)&&u(t[e])}}}();__ez.evt.add=function(e,t,n){e.addEventListener?e.addEventListener(t,n,!1):e.attachEvent?e.attachEvent("on"+t,n):e["on"+t]=n()},__ez.evt.remove=function(e,t,n){e.removeEventListener?e.removeEventListener(t,n,!1):e.detachEvent?e.detachEvent("on"+t,n):delete e["on"+t]};__ez.script.add=function(e){var t=document.createElement("script");t.src=e,t.async=!0,t.type="text/javascript",document.getElementsByTagName("head")[0].appendChild(t)};__ez.dot={};__ez.queue.addFile('/detroitchicago/boise.js','/detroitchicago/boise.js?gcb=195-4&cb=5',true,[],true,false,true,false);__ez.queue.addFile('/parsonsmaize/abilene.js','/parsonsmaize/abilene.js?gcb=195-4&cb=b5ead80933',true,[],true,false,true,false);__ez.queue.addFile('/parsonsmaize/mulvane.js','/parsonsmaize/mulvane.js?gcb=195-4&cb=e75e48eec0',true,['/parsonsmaize/abilene.js'],true,false,true,false);__ez.queue.addFile('/detroitchicago/birmingham.js','/detroitchicago/birmingham.js?gcb=195-4&cb=539c47377c',true,['/parsonsmaize/abilene.js'],true,false,true,false);</script><script data-ezscrex=false data-cfasync=false>__ez.ssaf=[17,19,16];__ez.sswp=4;__ez.ssv=464444;__ez.sshsdef=true;</script><script data-ezscrex=false data-cfasync=false>__ez.queue.addFile('/tardisrocinante/screx.js','/tardisrocinante/screx.js?gcb=4&cb=5',false,['/detroitchicago/tulsa.js'],true,false,true,false);</script><script data-ezscrex=false data-cfasync=false>(function(){if("function"===typeof window.CustomEvent)return!1;window.CustomEvent=function(c,a){a=a||{bubbles:!1,cancelable:!1,detail:null};var b=document.createEvent("CustomEvent");b.initCustomEvent(c,a.bubbles,a.cancelable,a.detail);return b}})();</script><script data-ezscrex=false data-cfasync=false>__ez.queue.addFile('/detroitchicago/tulsa.js','/detroitchicago/tulsa.js?gcb=195-4&cb=9',false,[],true,false,true,false);</script><script data-ezscrex=false data-cfasync=false>window._ezaq=Object.assign({"ad_cache_level":1,"adpicker_placement_cnt":0,"ai_placeholder_cache_level":1,"ai_placeholder_placement_cnt":-1,"article_category":"Aussagen und Mengen","author":"Tamara","domain_id":140745,"ezcache_level":1,"ezcache_skip_code":0,"has_bad_image":0,"has_bad_words":0,"is_sitespeed":1,"lt_cache_level":0,"publish_date":"2018-03-20","response_size":181543,"response_size_orig":172814,"response_time_orig":878,"template_id":5,"url":"https://123mathe.de/mengenbegriff","word_count":0,"worst_bad_word_level":0},typeof window._ezaq!=="undefined"?window._ezaq:{});__ez.queue.markLoaded('ezaqBaseReady');</script><link rel=preconnect href=//gmpg.org crossorigin><link rel=preconnect href=//fonts.googleapis.com crossorigin><link rel=preconnect href=//www.brinkmann-du.de crossorigin><link rel=preconnect href=//vg06.met.vgwort.de crossorigin><link rel=preconnect href=//go.ezoic.net crossorigin><script data-ezscrex=false data-cfasync=false data-pagespeed-no-defer src="/tardisrocinante/cash.js?cb=4"></script><script data-ezscrex=false data-cfasync=false>window.ezAnalyticsStatic=true;function analyticsAddScript(script){var ezDynamic=document.createElement('script');ezDynamic.type='text/javascript';ezDynamic.innerHTML=script;document.head.appendChild(ezDynamic);} function getCookiesWithPrefix(){var allCookies=document.cookie.split(';');var cookiesWithPrefix={};for(var i=0;i<allCookies.length;i++){var cookie=allCookies[i].trim();for(var j=0;j<arguments.length;j++){var prefix=arguments[j];if(cookie.indexOf(prefix)===0){var cookieParts=cookie.split('=');var cookieName=cookieParts[0];var cookieValue=cookieParts.slice(1).join('=');cookiesWithPrefix[cookieName]=decodeURIComponent(cookieValue);break;}}} return cookiesWithPrefix;} function productAnalytics(){var d={"pr":[2,6],"omd5":"f3d58238310ac63b5f95783cca56baca","nar":"risk score"};d.u=_ezaq.url;d.p=_ezaq.page_view_id;d.v=_ezaq.visit_uuid;d.ab=_ezaq.ab_test_id;d.e=JSON.stringify(_ezaq);d.ref=document.referrer;d.c=getCookiesWithPrefix('active_template','ez','lp_');if(typeof ez_utmParams!=='undefined'){d.utm=ez_utmParams;} var dataText=JSON.stringify(d);var xhr=new XMLHttpRequest();xhr.open('POST','/ezais/analytics?cb=1',true);xhr.onload=function(){if(xhr.status!=200){return;} if(document.readyState!=='loading'){analyticsAddScript(xhr.response);return;} var eventFunc=function(){if(document.readyState==='loading'){return;} document.removeEventListener('readystatechange',eventFunc,false);analyticsAddScript(xhr.response);};document.addEventListener('readystatechange',eventFunc,false);};xhr.setRequestHeader('Content-Type','text/plain');xhr.send(dataText);} __ez.queue.addFunc("productAnalytics","productAnalytics",null,true,['ezaqBaseReady'],false,false,false,true);</script><base href=https://123mathe.de/mengenbegriff><meta name=viewport content="width=device-width,initial-scale=1"><link rel=profile href=https://gmpg.org/xfn/11><meta name=robots content="index, follow, max-image-preview:large, max-snippet:-1, max-video-preview:-1"><style>img:is([sizes=auto i],[sizes^="auto," i]){contain-intrinsic-size:3e3px 1500px}</style><title>Mengenbegriff in der Mengenlehre • 123mathe</title><meta name=description content="Einführung in die Mengenlehre, Mengenbegriff, Definition Menge, Darstellung von Mengen, Mengenschreibweise, Mengendiagramm, Beispiele"><link rel=canonical href=https://123mathe.de/mengenbegriff><meta property="og:locale" content="de_DE"><meta property="og:type" content="article"><meta property="og:title" content="Mengenbegriff in der Mengenlehre"><meta property="og:description" content="Einführung in die Mengenlehre, Mengenbegriff, Definition Menge, Darstellung von Mengen, Mengenschreibweise, Mengendiagramm, Beispiele"><meta property="og:url" content="https://123mathe.de/mengenbegriff"><meta property="og:site_name" content="123mathe"><meta property="article:publisher" content="https://www.facebook.com/Mathebrinkmann-257066754370078/"><meta property="article:author" content="https://www.facebook.com/charlotte.brinkmann.9/"><meta property="article:published_time" content="2018-03-20T10:11:59+00:00"><meta property="article:modified_time" content="2022-10-12T06:37:24+00:00"><meta property="og:image" content="https://www.brinkmann-du.de/mathe/fos/formel/f_560.gif"><meta name=author content="Tamara"><meta name=twitter:card content="summary_large_image"><meta name=twitter:creator content="@MatheBrinkmann"><meta name=twitter:site content="@MatheBrinkmann"><meta name=twitter:label1 content="Verfasst von"><meta name=twitter:data1 content="Tamara"><meta name=twitter:label2 content="Geschätzte Lesezeit"><meta name=twitter:data2 content="4 Minuten"><script type=application/ld+json class=yoast-schema-graph>{"@context":"https://schema.org","@graph":[{"@type":"ScholarlyArticle","@id":"https://123mathe.de/mengenbegriff#article","isPartOf":{"@id":"https://123mathe.de/mengenbegriff"},"author":{"name":"Tamara","@id":"https://123mathe.de/#/schema/person/95e188d55cce5386ec58e961129f8907"},"headline":"Mengenbegriff in der Mengenlehre","datePublished":"2018-03-20T10:11:59+00:00","dateModified":"2022-10-12T06:37:24+00:00","mainEntityOfPage":{"@id":"https://123mathe.de/mengenbegriff"},"wordCount":379,"publisher":{"@id":"https://123mathe.de/#organization"},"image":{"@id":"https://123mathe.de/mengenbegriff#primaryimage"},"thumbnailUrl":"https://www.brinkmann-du.de/mathe/fos/formel/f_560.gif","articleSection":["Aussagen und Mengen","Mathematik"],"inLanguage":"de"},{"@type":"WebPage","@id":"https://123mathe.de/mengenbegriff","url":"https://123mathe.de/mengenbegriff","name":"Mengenbegriff in der Mengenlehre • 123mathe","isPartOf":{"@id":"https://123mathe.de/#website"},"primaryImageOfPage":{"@id":"https://123mathe.de/mengenbegriff#primaryimage"},"image":{"@id":"https://123mathe.de/mengenbegriff#primaryimage"},"thumbnailUrl":"https://www.brinkmann-du.de/mathe/fos/formel/f_560.gif","datePublished":"2018-03-20T10:11:59+00:00","dateModified":"2022-10-12T06:37:24+00:00","description":"Einführung in die Mengenlehre, Mengenbegriff, Definition Menge, Darstellung von Mengen, Mengenschreibweise, Mengendiagramm, Beispiele","breadcrumb":{"@id":"https://123mathe.de/mengenbegriff#breadcrumb"},"inLanguage":"de","potentialAction":[{"@type":"ReadAction","target":["https://123mathe.de/mengenbegriff"]}]},{"@type":"ImageObject","inLanguage":"de","@id":"https://123mathe.de/mengenbegriff#primaryimage","url":"https://www.brinkmann-du.de/mathe/fos/formel/f_560.gif","contentUrl":"https://www.brinkmann-du.de/mathe/fos/formel/f_560.gif"},{"@type":"BreadcrumbList","@id":"https://123mathe.de/mengenbegriff#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Startseite","item":"https://123mathe.de/"},{"@type":"ListItem","position":2,"name":"Mathematik","item":"https://123mathe.de/category/mathematik"},{"@type":"ListItem","position":3,"name":"Mengenbegriff in der Mengenlehre"}]},{"@type":"WebSite","@id":"https://123mathe.de/#website","url":"https://123mathe.de/","name":"123mathe","description":"Mathematik und Physik für Schüler, Lehrer und Eltern","publisher":{"@id":"https://123mathe.de/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://123mathe.de/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"de"},{"@type":"Organization","@id":"https://123mathe.de/#organization","name":"123mathe","url":"https://123mathe.de/","logo":{"@type":"ImageObject","inLanguage":"de","@id":"https://123mathe.de/#/schema/logo/image/","url":"https://123mathe.de/wp-content/uploads/2022/12/123mahte-logo-gross.webp","contentUrl":"https://123mathe.de/wp-content/uploads/2022/12/123mahte-logo-gross.webp","width":272,"height":205,"caption":"123mathe"},"image":{"@id":"https://123mathe.de/#/schema/logo/image/"},"sameAs":["https://www.facebook.com/Mathebrinkmann-257066754370078/","https://x.com/MatheBrinkmann"]},{"@type":"Person","@id":"https://123mathe.de/#/schema/person/95e188d55cce5386ec58e961129f8907","name":"Tamara","description":"Die Artikel sind ursprünglich alle von Rudolf Brinkmann erstellt worden. Er hat erst Elektriker gelernt, danach Elektrotechnik studiert, danach erst Lehramt Mathematik und Physik. Deshalb war er ein Praktiker. Er hat sehr anschaulich unterrichtet und es war ihm wichtig, dass die Schüler viele Aufgaben rechnen. Nach seinem Tod habe ich, Charlotte Brinkmann, die Webseite übernommen. Ich bin Diplom-Pädagogin, Programmiererin und habe lange IT-Seminare gegeben. Deshalb weiß ich, wie man unterrichtet. In der Schule war ich immer sehr gut in Mathematik und Deutsch und ich habe zwei Romane geschrieben. Mit diesen Erfahrungen habe ich alle Artikel sprachlich geglättet, so dass sie leichter zu lesen sind.","sameAs":["http://samvana.de/","https://www.facebook.com/charlotte.brinkmann.9/"],"gender":"weiblich","knowsAbout":["Mathematik","Deutsch","Programmierung"],"knowsLanguage":["deutsch","englisch"]}]}</script><link rel=dns-prefetch href=//fonts.googleapis.com><link rel=alternate type=application/rss+xml title="123mathe » Feed" href=https://123mathe.de/feed><link rel=alternate type=application/rss+xml title="123mathe » Kommentar-Feed" href=https://123mathe.de/comments/feed><script type=text/ez-screx>window._wpemojiSettings={"baseUrl":"https:\/\/s.w.org\/images\/core\/emoji\/15.0.3\/72x72\/","ext":".png","svgUrl":"https:\/\/s.w.org\/images\/core\/emoji\/15.0.3\/svg\/","svgExt":".svg","source":{"concatemoji":"https:\/\/123mathe.de\/wp-includes\/js\/wp-emoji-release.min.js?ver=6.7.2"}};/*!This file is auto-generated*/!function(i,n){var o,s,e;function c(e){try{var t={supportTests:e,timestamp:(new Date).valueOf()};sessionStorage.setItem(o,JSON.stringify(t))}catch(e){}}function p(e,t,n){e.clearRect(0,0,e.canvas.width,e.canvas.height),e.fillText(t,0,0);var t=new Uint32Array(e.getImageData(0,0,e.canvas.width,e.canvas.height).data),r=(e.clearRect(0,0,e.canvas.width,e.canvas.height),e.fillText(n,0,0),new Uint32Array(e.getImageData(0,0,e.canvas.width,e.canvas.height).data));return t.every(function(e,t){return e===r[t]})}function u(e,t,n){switch(t){case"flag":return n(e,"\ud83c\udff3\ufe0f\u200d\u26a7\ufe0f","\ud83c\udff3\ufe0f\u200b\u26a7\ufe0f")?!1:!n(e,"\ud83c\uddfa\ud83c\uddf3","\ud83c\uddfa\u200b\ud83c\uddf3")&&!n(e,"\ud83c\udff4\udb40\udc67\udb40\udc62\udb40\udc65\udb40\udc6e\udb40\udc67\udb40\udc7f","\ud83c\udff4\u200b\udb40\udc67\u200b\udb40\udc62\u200b\udb40\udc65\u200b\udb40\udc6e\u200b\udb40\udc67\u200b\udb40\udc7f");case"emoji":return!n(e,"\ud83d\udc26\u200d\u2b1b","\ud83d\udc26\u200b\u2b1b")}return!1}function f(e,t,n){var r="undefined"!=typeof WorkerGlobalScope&&self instanceof WorkerGlobalScope?new OffscreenCanvas(300,150):i.createElement("canvas"),a=r.getContext("2d",{willReadFrequently:!0}),o=(a.textBaseline="top",a.font="600 32px Arial",{});return e.forEach(function(e){o[e]=t(a,e,n)}),o}function t(e){var t=i.createElement("script");t.src=e,t.defer=!0,i.head.appendChild(t)}"undefined"!=typeof Promise&&(o="wpEmojiSettingsSupports",s=["flag","emoji"],n.supports={everything:!0,everythingExceptFlag:!0},e=new Promise(function(e){i.addEventListener("DOMContentLoaded",e,{once:!0})}),new Promise(function(t){var n=function(){try{var e=JSON.parse(sessionStorage.getItem(o));if("object"==typeof e&&"number"==typeof e.timestamp&&(new Date).valueOf()<e.timestamp+604800&&"object"==typeof e.supportTests)return e.supportTests}catch(e){}return null}();if(!n){if("undefined"!=typeof Worker&&"undefined"!=typeof OffscreenCanvas&&"undefined"!=typeof URL&&URL.createObjectURL&&"undefined"!=typeof Blob)try{var e="postMessage("+f.toString()+"("+[JSON.stringify(s),u.toString(),p.toString()].join(",")+"));",r=new Blob([e],{type:"text/javascript"}),a=new Worker(URL.createObjectURL(r),{name:"wpTestEmojiSupports"});return void(a.onmessage=function(e){c(n=e.data),a.terminate(),t(n)})}catch(e){}c(n=f(s,u,p))}t(n)}).then(function(e){for(var t in e)n.supports[t]=e[t],n.supports.everything=n.supports.everything&&n.supports[t],"flag"!==t&&(n.supports.everythingExceptFlag=n.supports.everythingExceptFlag&&n.supports[t]);n.supports.everythingExceptFlag=n.supports.everythingExceptFlag&&!n.supports.flag,n.DOMReady=!1,n.readyCallback=function(){n.DOMReady=!0}}).then(function(){return e}).then(function(){var e;n.supports.everything||(n.readyCallback(),(e=n.source||{}).concatemoji?t(e.concatemoji):e.wpemoji&&e.twemoji&&(t(e.twemoji),t(e.wpemoji)))}))}((window,document),window._wpemojiSettings);</script><link rel=stylesheet id=astra-theme-css-css href="https://123mathe.de/wp-content/themes/astra/assets/css/minified/main.min.css?ezmin=true&ff=1&ver=4.8.12&wps=false" media=all><style id=astra-theme-css-inline-css>:root{--ast-post-nav-space:0;--ast-container-default-xlg-padding:3em;--ast-container-default-lg-padding:3em;--ast-container-default-slg-padding:2em;--ast-container-default-md-padding:3em;--ast-container-default-sm-padding:3em;--ast-container-default-xs-padding:2.4em;--ast-container-default-xxs-padding:1.8em;--ast-code-block-background:#EEEEEE;--ast-comment-inputs-background:#FAFAFA;--ast-normal-container-width:1200px;--ast-narrow-container-width:750px;--ast-blog-title-font-weight:normal;--ast-blog-meta-weight:inherit;--ast-global-color-primary:var(--ast-global-color-5);--ast-global-color-secondary:var(--ast-global-color-4);--ast-global-color-alternate-background:var(--ast-global-color-7);--ast-global-color-subtle-background:var(--ast-global-color-6)}html{font-size:106.25%}a{color:#cd2653}a:hover,a:focus{color:#000}body,button,input,select,textarea,.ast-button,.ast-custom-button{font-family:karla,sans-serif;font-weight:inherit;font-size:17px;font-size:1rem}blockquote{color:#000}h1,.entry-content h1,h2,.entry-content h2,h3,.entry-content h3,h4,.entry-content h4,h5,.entry-content h5,h6,.entry-content h6,.site-title,.site-title a{font-family:rubik,sans-serif;font-weight:600}.site-title{font-size:35px;font-size:2.05882352941rem;display:block}.site-header .site-description{font-size:15px;font-size:.882352941176rem;display:block}.entry-title{font-size:30px;font-size:1.76470588235rem}.archive .ast-article-post .ast-article-inner,.blog .ast-article-post .ast-article-inner,.archive .ast-article-post .ast-article-inner:hover,.blog .ast-article-post .ast-article-inner:hover{overflow:hidden}h1,.entry-content h1{font-size:48px;font-size:2.82352941176rem;font-weight:600;font-family:rubik,sans-serif;line-height:1.4em}h2,.entry-content h2{font-size:38px;font-size:2.23529411765rem;font-weight:600;font-family:rubik,sans-serif;line-height:1.3em}h3,.entry-content h3{font-size:30px;font-size:1.76470588235rem;font-weight:600;font-family:rubik,sans-serif;line-height:1.3em}h4,.entry-content h4{font-size:24px;font-size:1.41176470588rem;line-height:1.2em;font-weight:600;font-family:rubik,sans-serif}h5,.entry-content h5{font-size:21px;font-size:1.23529411765rem;line-height:1.2em;font-weight:600;font-family:rubik,sans-serif}h6,.entry-content h6{font-size:17px;font-size:1rem;line-height:1.25em;font-weight:600;font-family:rubik,sans-serif}::selection{background-color:#cd2653;color:#fff}body,h1,.entry-title a,.entry-content h1,h2,.entry-content h2,h3,.entry-content h3,h4,.entry-content h4,h5,.entry-content h5,h6,.entry-content h6{color:#000}.tagcloud a:hover,.tagcloud a:focus,.tagcloud a.current-item{color:#fff;border-color:#cd2653;background-color:#cd2653}input:focus,input[type=text]:focus,input[type=email]:focus,input[type=url]:focus,input[type=password]:focus,input[type=reset]:focus,input[type=search]:focus,textarea:focus{border-color:#cd2653}input[type=radio]:checked,input[type=reset],input[type=checkbox]:checked,input[type=checkbox]:hover:checked,input[type=checkbox]:focus:checked,input[type=range]::-webkit-slider-thumb{border-color:#cd2653;background-color:#cd2653;box-shadow:0 0}.site-footer a:hover+.post-count,.site-footer a:focus+.post-count{background:#cd2653;border-color:#cd2653}.single .nav-links .nav-previous,.single .nav-links .nav-next{color:#cd2653}.entry-meta,.entry-meta *{line-height:1.45;color:#cd2653}.entry-meta a:not(.ast-button):hover,.entry-meta a:not(.ast-button):hover *,.entry-meta a:not(.ast-button):focus,.entry-meta a:not(.ast-button):focus *,.page-links>.page-link,.page-links .page-link:hover,.post-navigation a:hover{color:#000}#cat option,.secondary .calendar_wrap thead a,.secondary .calendar_wrap thead a:visited{color:#cd2653}.secondary .calendar_wrap #today,.ast-progress-val span{background:#cd2653}.secondary a:hover+.post-count,.secondary a:focus+.post-count{background:#cd2653;border-color:#cd2653}.calendar_wrap #today>a{color:#fff}.page-links .page-link,.single .post-navigation a{color:#cd2653}.ast-search-menu-icon .search-form button.search-submit{padding:0 4px}.ast-search-menu-icon form.search-form{padding-right:0}.ast-search-menu-icon.slide-search input.search-field{width:0}.ast-header-search .ast-search-menu-icon.ast-dropdown-active .search-form,.ast-header-search .ast-search-menu-icon.ast-dropdown-active .search-field:focus{transition:all .2s}.search-form input.search-field:focus{outline:none}.ast-archive-title{color:#000}.widget-title,.widget .wp-block-heading{font-size:24px;font-size:1.41176470588rem;color:#000}.ast-single-post .entry-content a,.ast-comment-content a:not(.ast-comment-edit-reply-wrap a){text-decoration:underline}.ast-single-post .wp-block-button .wp-block-button__link,.ast-single-post .elementor-button-wrapper .elementor-button,.ast-single-post .entry-content .uagb-tab a,.ast-single-post .entry-content .uagb-ifb-cta a,.ast-single-post .entry-content .wp-block-uagb-buttons a,.ast-single-post .entry-content .uabb-module-content a,.ast-single-post .entry-content .uagb-post-grid a,.ast-single-post .entry-content .uagb-timeline a,.ast-single-post .entry-content .uagb-toc__wrap a,.ast-single-post .entry-content .uagb-taxomony-box a,.ast-single-post .entry-content .woocommerce a,.entry-content .wp-block-latest-posts>li>a,.ast-single-post .entry-content .wp-block-file__button,li.ast-post-filter-single,.ast-single-post .wp-block-buttons .wp-block-button.is-style-outline .wp-block-button__link,.ast-single-post .ast-comment-content .comment-reply-link,.ast-single-post .ast-comment-content .comment-edit-link{text-decoration:none}.ast-search-menu-icon.slide-search a:focus-visible:focus-visible,.astra-search-icon:focus-visible,#close:focus-visible,a:focus-visible,.ast-menu-toggle:focus-visible,.site .skip-link:focus-visible,.wp-block-loginout input:focus-visible,.wp-block-search.wp-block-search__button-inside .wp-block-search__inside-wrapper,.ast-header-navigation-arrow:focus-visible,.woocommerce .wc-proceed-to-checkout>.checkout-button:focus-visible,.woocommerce .woocommerce-MyAccount-navigation ul li a:focus-visible,.ast-orders-table__row .ast-orders-table__cell:focus-visible,.woocommerce .woocommerce-order-details .order-again>.button:focus-visible,.woocommerce .woocommerce-message a.button.wc-forward:focus-visible,.woocommerce #minus_qty:focus-visible,.woocommerce #plus_qty:focus-visible,a#ast-apply-coupon:focus-visible,.woocommerce .woocommerce-info a:focus-visible,.woocommerce .astra-shop-summary-wrap a:focus-visible,.woocommerce a.wc-forward:focus-visible,#ast-apply-coupon:focus-visible,.woocommerce-js .woocommerce-mini-cart-item a.remove:focus-visible,#close:focus-visible,.button.search-submit:focus-visible,#search_submit:focus,.normal-search:focus-visible,.ast-header-account-wrap:focus-visible,.woocommerce .ast-on-card-button.ast-quick-view-trigger:focus{outline-style:dotted;outline-color:inherit;outline-width:thin}input:focus,input[type=text]:focus,input[type=email]:focus,input[type=url]:focus,input[type=password]:focus,input[type=reset]:focus,input[type=search]:focus,input[type=number]:focus,textarea:focus,.wp-block-search__input:focus,[data-section=section-header-mobile-trigger] .ast-button-wrap .ast-mobile-menu-trigger-minimal:focus,.ast-mobile-popup-drawer.active .menu-toggle-close:focus,.woocommerce-ordering select.orderby:focus,#ast-scroll-top:focus,#coupon_code:focus,.woocommerce-page #comment:focus,.woocommerce #reviews #respond input#submit:focus,.woocommerce a.add_to_cart_button:focus,.woocommerce .button.single_add_to_cart_button:focus,.woocommerce .woocommerce-cart-form button:focus,.woocommerce .woocommerce-cart-form__cart-item .quantity .qty:focus,.woocommerce .woocommerce-billing-fields .woocommerce-billing-fields__field-wrapper .woocommerce-input-wrapper>.input-text:focus,.woocommerce #order_comments:focus,.woocommerce #place_order:focus,.woocommerce .woocommerce-address-fields .woocommerce-address-fields__field-wrapper .woocommerce-input-wrapper>.input-text:focus,.woocommerce .woocommerce-MyAccount-content form button:focus,.woocommerce .woocommerce-MyAccount-content .woocommerce-EditAccountForm .woocommerce-form-row .woocommerce-Input.input-text:focus,.woocommerce .ast-woocommerce-container .woocommerce-pagination ul.page-numbers li a:focus,body #content .woocommerce form .form-row .select2-container--default .select2-selection--single:focus,#ast-coupon-code:focus,.woocommerce.woocommerce-js .quantity input[type=number]:focus,.woocommerce-js .woocommerce-mini-cart-item .quantity input[type=number]:focus,.woocommerce p#ast-coupon-trigger:focus{border-style:dotted;border-color:inherit;border-width:thin}input{outline:none}.ast-logo-title-inline .site-logo-img{padding-right:1em}body .ast-oembed-container *{position:absolute;top:0;width:100%;height:100%;left:0}body .wp-block-embed-pocket-casts .ast-oembed-container *{position:unset}.ast-single-post-featured-section+article{margin-top:2em}.site-content .ast-single-post-featured-section img{width:100%;overflow:hidden;object-fit:cover}.site>.ast-single-related-posts-container{margin-top:0}@media(min-width:922px){.ast-desktop .ast-container--narrow{max-width:var(--ast-narrow-container-width);margin:0 auto}}@media(max-width:921.9px){#ast-desktop-header{display:none}}@media(min-width:922px){#ast-mobile-header{display:none}}@media(max-width:420px){.single .nav-links .nav-previous,.single .nav-links .nav-next{width:100%;text-align:center}}.wp-block-buttons.aligncenter{justify-content:center}@media(max-width:921px){.ast-theme-transparent-header #primary,.ast-theme-transparent-header #secondary{padding:0}}@media(max-width:921px){.ast-plain-container.ast-no-sidebar #primary{padding:0}}.ast-plain-container.ast-no-sidebar #primary{margin-top:0;margin-bottom:0}@media(min-width:1200px){.ast-plain-container.ast-no-sidebar #primary{margin-top:60px;margin-bottom:60px}}.ast-separate-container.ast-single-post.ast-right-sidebar #primary,.ast-separate-container.ast-single-post.ast-left-sidebar #primary,.ast-separate-container.ast-single-post #primary,.ast-plain-container.ast-single-post #primary,.ast-narrow-container.ast-single-post #primary{margin-top:45px;margin-bottom:0}.ast-left-sidebar.ast-single-post #primary,.ast-right-sidebar.ast-single-post #primary,.ast-separate-container.ast-single-post.ast-right-sidebar #primary,.ast-separate-container.ast-single-post.ast-left-sidebar #primary,.ast-separate-container.ast-single-post #primary,.ast-narrow-container.ast-single-post #primary{padding-left:0;padding-right:0}.ast-separate-container #primary,.ast-narrow-container #primary{padding-top:0}.ast-separate-container #primary,.ast-narrow-container #primary{padding-bottom:0}.wp-block-button.is-style-outline .wp-block-button__link{border-color:rgba(204,39,83,.48);border-top-width:0;border-right-width:0;border-bottom-width:0;border-left-width:0}div.wp-block-button.is-style-outline>.wp-block-button__link:not(.has-text-color),div.wp-block-button.wp-block-button__link.is-style-outline:not(.has-text-color){color:rgba(204,39,83,.48)}.wp-block-button.is-style-outline .wp-block-button__link:hover,.wp-block-buttons .wp-block-button.is-style-outline .wp-block-button__link:focus,.wp-block-buttons .wp-block-button.is-style-outline>.wp-block-button__link:not(.has-text-color):hover,.wp-block-buttons .wp-block-button.wp-block-button__link.is-style-outline:not(.has-text-color):hover{color:var(--ast-global-color-5);background-color:#cd2653;border-color:#cd2653}.post-page-numbers.current .page-link,.ast-pagination .page-numbers.current{color:#fff;border-color:#cd2653;background-color:#cd2653}.wp-block-button.is-style-outline .wp-block-button__link{border-top-width:0;border-right-width:0;border-bottom-width:0;border-left-width:0}.wp-block-button.is-style-outline .wp-block-button__link.wp-element-button,.ast-outline-button{border-color:rgba(204,39,83,.48);font-family:inherit;font-weight:inherit;line-height:1em;border-top-left-radius:30px;border-top-right-radius:30px;border-bottom-right-radius:30px;border-bottom-left-radius:30px}.wp-block-buttons .wp-block-button.is-style-outline>.wp-block-button__link:not(.has-text-color),.wp-block-buttons .wp-block-button.wp-block-button__link.is-style-outline:not(.has-text-color),.ast-outline-button{color:rgba(204,39,83,.48)}.wp-block-button.is-style-outline .wp-block-button__link:hover,.wp-block-buttons .wp-block-button.is-style-outline .wp-block-button__link:focus,.wp-block-buttons .wp-block-button.is-style-outline>.wp-block-button__link:not(.has-text-color):hover,.wp-block-buttons .wp-block-button.wp-block-button__link.is-style-outline:not(.has-text-color):hover,.ast-outline-button:hover,.ast-outline-button:focus,.wp-block-uagb-buttons-child .uagb-buttons-repeater.ast-outline-button:hover,.wp-block-uagb-buttons-child .uagb-buttons-repeater.ast-outline-button:focus{color:var(--ast-global-color-5);background-color:#cd2653;border-color:#cd2653}.wp-block-button .wp-block-button__link.wp-element-button.is-style-outline:not(.has-background),.wp-block-button.is-style-outline>.wp-block-button__link.wp-element-button:not(.has-background),.ast-outline-button{background-color:rgba(204,39,83,.48)}.entry-content[data-ast-blocks-layout]>figure{margin-bottom:1em}h1.widget-title{font-weight:600}h2.widget-title{font-weight:600}h3.widget-title{font-weight:600}#page{display:flex;flex-direction:column;min-height:100vh}.ast-404-layout-1 h1.page-title{color:var(--ast-global-color-2)}.single .post-navigation a{line-height:1em;height:inherit}.error-404 .page-sub-title{font-size:1.5rem;font-weight:inherit}.search .site-content .content-area .search-form{margin-bottom:0}#page .site-content{flex-grow:1}.widget{margin-bottom:1.25em}#secondary li{line-height:1.5em}#secondary .wp-block-group h2{margin-bottom:.7em}#secondary h2{font-size:1.7rem}.ast-separate-container .ast-article-post,.ast-separate-container .ast-article-single,.ast-separate-container .comment-respond{padding:3em}.ast-separate-container .ast-article-single .ast-article-single{padding:0}.ast-article-single .wp-block-post-template-is-layout-grid{padding-left:0}.ast-separate-container .comments-title,.ast-narrow-container .comments-title{padding:1.5em 2em}.ast-page-builder-template .comment-form-textarea,.ast-comment-formwrap .ast-grid-common-col{padding:0}.ast-comment-formwrap{padding:0;display:inline-flex;column-gap:20px;width:100%;margin-left:0;margin-right:0}.comments-area textarea#comment:focus,.comments-area textarea#comment:active,.comments-area .ast-comment-formwrap input[type=text]:focus,.comments-area .ast-comment-formwrap input[type=text]:active{box-shadow:0 0;outline:none}.archive.ast-page-builder-template .entry-header{margin-top:2em}.ast-page-builder-template .ast-comment-formwrap{width:100%}.entry-title{margin-bottom:.5em}.ast-archive-description p{font-size:inherit;font-weight:inherit;line-height:inherit}.ast-separate-container .ast-comment-list li.depth-1,.hentry{margin-bottom:2em}@media(min-width:921px){.ast-left-sidebar.ast-page-builder-template #secondary,.archive.ast-right-sidebar.ast-page-builder-template .site-main{padding-left:20px;padding-right:20px}}@media(max-width:544px){.ast-comment-formwrap.ast-row{column-gap:10px;display:inline-block}#ast-commentform .ast-grid-common-col{position:relative;width:100%}}@media(min-width:1201px){.ast-separate-container .ast-article-post,.ast-separate-container .ast-article-single,.ast-separate-container .ast-author-box,.ast-separate-container .ast-404-layout-1,.ast-separate-container .no-results{padding:3em}}@media(max-width:921px){.ast-separate-container #primary,.ast-separate-container #secondary{padding:1.5em 0}#primary,#secondary{padding:1.5em 0;margin:0}.ast-left-sidebar #content>.ast-container{display:flex;flex-direction:column-reverse;width:100%}}@media(min-width:922px){.ast-separate-container.ast-right-sidebar #primary,.ast-separate-container.ast-left-sidebar #primary{border:0}.search-no-results.ast-separate-container #primary{margin-bottom:4em}}.wp-block-button .wp-block-button__link{color:var(--ast-global-color-5)}.wp-block-button .wp-block-button__link:hover,.wp-block-button .wp-block-button__link:focus{color:var(--ast-global-color-5);background-color:#cd2653;border-color:#cd2653}.wp-block-button .wp-block-button__link,.wp-block-search .wp-block-search__button,body .wp-block-file .wp-block-file__button{border-top-width:0;border-right-width:0;border-left-width:0;border-bottom-width:0;border-color:rgba(204,39,83,.48);background-color:rgba(204,39,83,.48);color:var(--ast-global-color-5);font-family:inherit;font-weight:inherit;line-height:1em;border-top-left-radius:30px;border-top-right-radius:30px;border-bottom-right-radius:30px;border-bottom-left-radius:30px;padding-top:10px;padding-right:20px;padding-bottom:10px;padding-left:20px}.menu-toggle,button,.ast-button,.ast-custom-button,.button,input#submit,input[type=button],input[type=submit],input[type=reset],form[CLASS*=wp-block-search__].wp-block-search .wp-block-search__inside-wrapper .wp-block-search__button,body .wp-block-file .wp-block-file__button,.search .search-submit{border-style:solid;border-top-width:0;border-right-width:0;border-left-width:0;border-bottom-width:0;color:var(--ast-global-color-5);border-color:rgba(204,39,83,.48);background-color:rgba(204,39,83,.48);padding-top:10px;padding-right:20px;padding-bottom:10px;padding-left:20px;font-family:inherit;font-weight:inherit;line-height:1em;border-top-left-radius:30px;border-top-right-radius:30px;border-bottom-right-radius:30px;border-bottom-left-radius:30px}button:focus,.menu-toggle:hover,button:hover,.ast-button:hover,.ast-custom-button:hover .button:hover,.ast-custom-button:hover,input[type=reset]:hover,input[type=reset]:focus,input#submit:hover,input#submit:focus,input[type=button]:hover,input[type=button]:focus,input[type=submit]:hover,input[type=submit]:focus,form[CLASS*=wp-block-search__].wp-block-search .wp-block-search__inside-wrapper .wp-block-search__button:hover,form[CLASS*=wp-block-search__].wp-block-search .wp-block-search__inside-wrapper .wp-block-search__button:focus,body .wp-block-file .wp-block-file__button:hover,body .wp-block-file .wp-block-file__button:focus{color:var(--ast-global-color-5);background-color:#cd2653;border-color:#cd2653}form[CLASS*=wp-block-search__].wp-block-search .wp-block-search__inside-wrapper .wp-block-search__button.has-icon{padding-top:calc(10px - 3px);padding-right:calc(20px - 3px);padding-bottom:calc(10px - 3px);padding-left:calc(20px - 3px)}@media(max-width:921px){.ast-mobile-header-stack .main-header-bar .ast-search-menu-icon{display:inline-block}.ast-header-break-point.ast-header-custom-item-outside .ast-mobile-header-stack .main-header-bar .ast-search-icon{margin:0}.ast-comment-avatar-wrap img{max-width:2.5em}.ast-comment-meta{padding:0 1.8888em 1.3333em}.ast-separate-container .ast-comment-list li.depth-1{padding:1.5em 2.14em}.ast-separate-container .comment-respond{padding:2em 2.14em}}@media(min-width:544px){.ast-container{max-width:100%}}@media(max-width:544px){.ast-separate-container .ast-article-post,.ast-separate-container .ast-article-single,.ast-separate-container .comments-title,.ast-separate-container .ast-archive-description{padding:1.5em 1em}.ast-separate-container #content .ast-container{padding-left:.54em;padding-right:.54em}.ast-separate-container .ast-comment-list .bypostauthor{padding:.5em}.ast-search-menu-icon.ast-dropdown-active .search-field{width:170px}}@media(max-width:921px){.ast-header-break-point .ast-search-menu-icon.slide-search .search-form{right:0}.ast-header-break-point .ast-mobile-header-stack .ast-search-menu-icon.slide-search .search-form{right:-1em}}#ast-mobile-header .ast-site-header-cart-li a{pointer-events:none}.ast-separate-container{background-color:var(--ast-global-color-5);background-image:none}@media(max-width:921px){.widget-title{font-size:24px;font-size:1.41176470588rem}body,button,input,select,textarea,.ast-button,.ast-custom-button{font-size:17px;font-size:1rem}#secondary,#secondary button,#secondary input,#secondary select,#secondary textarea{font-size:17px;font-size:1rem}.site-title{display:block}.site-header .site-description{display:block}.entry-title{font-size:35px;font-size:2.05882352941rem}h1,.entry-content h1{font-size:40px}h2,.entry-content h2{font-size:32px}h3,.entry-content h3{font-size:26px}h4,.entry-content h4{font-size:20px;font-size:1.17647058824rem}h5,.entry-content h5{font-size:17px;font-size:1rem}h6,.entry-content h6{font-size:15px;font-size:.882352941176rem}body,.ast-separate-container{background-color:var(--ast-global-color-5);background-image:none}}@media(max-width:544px){.widget-title{font-size:24px;font-size:1.41176470588rem}body,button,input,select,textarea,.ast-button,.ast-custom-button{font-size:17px;font-size:1rem}#secondary,#secondary button,#secondary input,#secondary select,#secondary textarea{font-size:17px;font-size:1rem}.site-title{display:block}.site-header .site-description{display:none}.entry-title{font-size:25px;font-size:1.47058823529rem}h1,.entry-content h1{font-size:36px}h2,.entry-content h2{font-size:28px}h3,.entry-content h3{font-size:22px}h4,.entry-content h4{font-size:18px;font-size:1.05882352941rem}h5,.entry-content h5{font-size:15px;font-size:.882352941176rem}h6,.entry-content h6{font-size:14px;font-size:.823529411765rem}body,.ast-separate-container{background-color:var(--ast-global-color-5);background-image:none}}@media(max-width:544px){html{font-size:106.25%}}@media(min-width:922px){.ast-container{max-width:1240px}}@media(min-width:922px){.site-content .ast-container{display:flex}}@media(max-width:921px){.site-content .ast-container{flex-direction:column}}@media(min-width:922px){.main-header-menu .sub-menu .menu-item.ast-left-align-sub-menu:hover>.sub-menu,.main-header-menu .sub-menu .menu-item.ast-left-align-sub-menu.focus>.sub-menu{margin-left:0}}.site .comments-area{padding-bottom:3em}.wp-block-file{display:flex;align-items:center;flex-wrap:wrap;justify-content:space-between}.wp-block-pullquote{border:none}.wp-block-pullquote blockquote::before{content:"\201D";font-family:helvetica,sans-serif;display:flex;transform:rotate( 180deg );font-size:6rem;font-style:normal;line-height:1;font-weight:700;align-items:center;justify-content:center}.has-text-align-right>blockquote::before{justify-content:flex-start}.has-text-align-left>blockquote::before{justify-content:flex-end}figure.wp-block-pullquote.is-style-solid-color blockquote{max-width:100%;text-align:inherit}:root{--wp--custom--ast-default-block-top-padding:3em;--wp--custom--ast-default-block-right-padding:3em;--wp--custom--ast-default-block-bottom-padding:3em;--wp--custom--ast-default-block-left-padding:3em;--wp--custom--ast-container-width:1200px;--wp--custom--ast-content-width-size:1200px;--wp--custom--ast-wide-width-size:calc(1200px + var(--wp--custom--ast-default-block-left-padding) + var(--wp--custom--ast-default-block-right-padding))}.ast-narrow-container{--wp--custom--ast-content-width-size:750px;--wp--custom--ast-wide-width-size:750px}@media(max-width:921px){:root{--wp--custom--ast-default-block-top-padding:3em;--wp--custom--ast-default-block-right-padding:2em;--wp--custom--ast-default-block-bottom-padding:3em;--wp--custom--ast-default-block-left-padding:2em}}@media(max-width:544px){:root{--wp--custom--ast-default-block-top-padding:3em;--wp--custom--ast-default-block-right-padding:1.5em;--wp--custom--ast-default-block-bottom-padding:3em;--wp--custom--ast-default-block-left-padding:1.5em}}.entry-content>.wp-block-group,.entry-content>.wp-block-cover,.entry-content>.wp-block-columns{padding-top:var(--wp--custom--ast-default-block-top-padding);padding-right:var(--wp--custom--ast-default-block-right-padding);padding-bottom:var(--wp--custom--ast-default-block-bottom-padding);padding-left:var(--wp--custom--ast-default-block-left-padding)}.ast-plain-container.ast-no-sidebar .entry-content>.alignfull,.ast-page-builder-template .ast-no-sidebar .entry-content>.alignfull{margin-left:calc( -50vw + 50%);margin-right:calc( -50vw + 50%);max-width:100vw;width:100vw}.ast-plain-container.ast-no-sidebar .entry-content .alignfull .alignfull,.ast-page-builder-template.ast-no-sidebar .entry-content .alignfull .alignfull,.ast-plain-container.ast-no-sidebar .entry-content .alignfull .alignwide,.ast-page-builder-template.ast-no-sidebar .entry-content .alignfull .alignwide,.ast-plain-container.ast-no-sidebar .entry-content .alignwide .alignfull,.ast-page-builder-template.ast-no-sidebar .entry-content .alignwide .alignfull,.ast-plain-container.ast-no-sidebar .entry-content .alignwide .alignwide,.ast-page-builder-template.ast-no-sidebar .entry-content .alignwide .alignwide,.ast-plain-container.ast-no-sidebar .entry-content .wp-block-column .alignfull,.ast-page-builder-template.ast-no-sidebar .entry-content .wp-block-column .alignfull,.ast-plain-container.ast-no-sidebar .entry-content .wp-block-column .alignwide,.ast-page-builder-template.ast-no-sidebar .entry-content .wp-block-column .alignwide{margin-left:auto;margin-right:auto;width:100%}[data-ast-blocks-layout] .wp-block-separator:not(.is-style-dots){height:0}[data-ast-blocks-layout] .wp-block-separator{margin:20px auto}[data-ast-blocks-layout] .wp-block-separator:not(.is-style-wide):not(.is-style-dots){max-width:100px}[data-ast-blocks-layout] .wp-block-separator.has-background{padding:0}.entry-content[data-ast-blocks-layout]>*{max-width:var(--wp--custom--ast-content-width-size);margin-left:auto;margin-right:auto}.entry-content[data-ast-blocks-layout]>.alignwide{max-width:var(--wp--custom--ast-wide-width-size)}.entry-content[data-ast-blocks-layout] .alignfull{max-width:none}.entry-content .wp-block-columns{margin-bottom:0}blockquote{margin:1.5em;border-color:rgba(0,0,0,5%)}.wp-block-quote:not(.has-text-align-right):not(.has-text-align-center){border-left:5px solid rgba(0,0,0,5%)}.has-text-align-right>blockquote,blockquote.has-text-align-right{border-right:5px solid rgba(0,0,0,5%)}.has-text-align-left>blockquote,blockquote.has-text-align-left{border-left:5px solid rgba(0,0,0,5%)}.wp-block-site-tagline,.wp-block-latest-posts .read-more{margin-top:15px}.wp-block-loginout p label{display:block}.wp-block-loginout p:not(.login-remember):not(.login-submit) input{width:100%}.wp-block-loginout input:focus{border-color:transparent}.wp-block-loginout input:focus{outline:thin dotted}.entry-content .wp-block-media-text .wp-block-media-text__content{padding:0 0 0 8%}.entry-content .wp-block-media-text.has-media-on-the-right .wp-block-media-text__content{padding:0 8% 0 0}.entry-content .wp-block-media-text.has-background .wp-block-media-text__content{padding:8%}.entry-content .wp-block-cover:not([class*=background-color]):not(.has-text-color.has-link-color) .wp-block-cover__inner-container,.entry-content .wp-block-cover:not([class*=background-color]) .wp-block-cover-image-text,.entry-content .wp-block-cover:not([class*=background-color]) .wp-block-cover-text,.entry-content .wp-block-cover-image:not([class*=background-color]) .wp-block-cover__inner-container,.entry-content .wp-block-cover-image:not([class*=background-color]) .wp-block-cover-image-text,.entry-content .wp-block-cover-image:not([class*=background-color]) .wp-block-cover-text{color:var(--ast-global-color-primary,var(--ast-global-color-5))}.wp-block-loginout .login-remember input{width:1.1rem;height:1.1rem;margin:0 5px 4px 0;vertical-align:middle}.wp-block-latest-posts>li>*:first-child,.wp-block-latest-posts:not(.is-grid)>li:first-child{margin-top:0}.entry-content>.wp-block-buttons,.entry-content>.wp-block-uagb-buttons{margin-bottom:1.5em}.wp-block-search__inside-wrapper .wp-block-search__input{padding:0 10px;color:var(--ast-global-color-3);background:var(--ast-global-color-primary,var(--ast-global-color-5));border-color:var(--ast-border-color)}.wp-block-latest-posts .read-more{margin-bottom:1.5em}.wp-block-search__no-button .wp-block-search__inside-wrapper .wp-block-search__input{padding-top:5px;padding-bottom:5px}.wp-block-latest-posts .wp-block-latest-posts__post-date,.wp-block-latest-posts .wp-block-latest-posts__post-author{font-size:1rem}.wp-block-latest-posts>li>*,.wp-block-latest-posts:not(.is-grid)>li{margin-top:12px;margin-bottom:12px}.ast-page-builder-template .entry-content[data-ast-blocks-layout]>*,.ast-page-builder-template .entry-content[data-ast-blocks-layout]>.alignfull:not(.wp-block-group):not(.uagb-is-root-container)>*{max-width:none}.ast-page-builder-template .entry-content[data-ast-blocks-layout]>.alignwide:not(.uagb-is-root-container)>*{max-width:var(--wp--custom--ast-wide-width-size)}.ast-page-builder-template .entry-content[data-ast-blocks-layout]>.inherit-container-width>*,.ast-page-builder-template .entry-content[data-ast-blocks-layout]>*:not(.wp-block-group):not(.uagb-is-root-container)>*,.entry-content[data-ast-blocks-layout]>.wp-block-cover .wp-block-cover__inner-container{max-width:var(--wp--custom--ast-content-width-size);margin-left:auto;margin-right:auto}.entry-content[data-ast-blocks-layout] .wp-block-cover:not(.alignleft):not(.alignright){width:auto}@media(max-width:1200px){.ast-separate-container .entry-content>.alignfull,.ast-separate-container .entry-content[data-ast-blocks-layout]>.alignwide,.ast-plain-container .entry-content[data-ast-blocks-layout]>.alignwide,.ast-plain-container .entry-content .alignfull{margin-left:calc(-1 * min(var(--ast-container-default-xlg-padding),20px));margin-right:calc(-1 * min(var(--ast-container-default-xlg-padding),20px))}}@media(min-width:1201px){.ast-separate-container .entry-content>.alignfull{margin-left:calc(-1 * var(--ast-container-default-xlg-padding) );margin-right:calc(-1 * var(--ast-container-default-xlg-padding) )}.ast-separate-container .entry-content[data-ast-blocks-layout]>.alignwide,.ast-plain-container .entry-content[data-ast-blocks-layout]>.alignwide{margin-left:calc(-1 * var(--wp--custom--ast-default-block-left-padding) );margin-right:calc(-1 * var(--wp--custom--ast-default-block-right-padding) )}}@media(min-width:921px){.ast-separate-container .entry-content .wp-block-group.alignwide:not(.inherit-container-width)>:where(:not(.alignleft):not(.alignright)),.ast-plain-container .entry-content .wp-block-group.alignwide:not(.inherit-container-width)>:where(:not(.alignleft):not(.alignright)){max-width:calc( var(--wp--custom--ast-content-width-size) + 80px )}.ast-plain-container.ast-right-sidebar .entry-content[data-ast-blocks-layout] .alignfull,.ast-plain-container.ast-left-sidebar .entry-content[data-ast-blocks-layout] .alignfull{margin-left:-60px;margin-right:-60px}}@media(min-width:544px){.entry-content>.alignleft{margin-right:20px}.entry-content>.alignright{margin-left:20px}}@media(max-width:544px){.wp-block-columns .wp-block-column:not(:last-child){margin-bottom:20px}.wp-block-latest-posts{margin:0}}@media(max-width:600px){.entry-content .wp-block-media-text .wp-block-media-text__content,.entry-content .wp-block-media-text.has-media-on-the-right .wp-block-media-text__content{padding:8% 0 0}.entry-content .wp-block-media-text.has-background .wp-block-media-text__content{padding:8%}}.ast-narrow-container .site-content .wp-block-uagb-image--align-full .wp-block-uagb-image__figure{max-width:100%;margin-left:auto;margin-right:auto}:root .has-ast-global-color-0-color{color:var(--ast-global-color-0)}:root .has-ast-global-color-0-background-color{background-color:var(--ast-global-color-0)}:root .wp-block-button .has-ast-global-color-0-color{color:var(--ast-global-color-0)}:root .wp-block-button .has-ast-global-color-0-background-color{background-color:var(--ast-global-color-0)}:root .has-ast-global-color-1-color{color:var(--ast-global-color-1)}:root .has-ast-global-color-1-background-color{background-color:var(--ast-global-color-1)}:root .wp-block-button .has-ast-global-color-1-color{color:var(--ast-global-color-1)}:root .wp-block-button .has-ast-global-color-1-background-color{background-color:var(--ast-global-color-1)}:root .has-ast-global-color-2-color{color:var(--ast-global-color-2)}:root .has-ast-global-color-2-background-color{background-color:var(--ast-global-color-2)}:root .wp-block-button .has-ast-global-color-2-color{color:var(--ast-global-color-2)}:root .wp-block-button .has-ast-global-color-2-background-color{background-color:var(--ast-global-color-2)}:root .has-ast-global-color-3-color{color:var(--ast-global-color-3)}:root .has-ast-global-color-3-background-color{background-color:var(--ast-global-color-3)}:root .wp-block-button .has-ast-global-color-3-color{color:var(--ast-global-color-3)}:root .wp-block-button .has-ast-global-color-3-background-color{background-color:var(--ast-global-color-3)}:root .has-ast-global-color-4-color{color:var(--ast-global-color-4)}:root .has-ast-global-color-4-background-color{background-color:var(--ast-global-color-4)}:root .wp-block-button .has-ast-global-color-4-color{color:var(--ast-global-color-4)}:root .wp-block-button .has-ast-global-color-4-background-color{background-color:var(--ast-global-color-4)}:root .has-ast-global-color-5-color{color:var(--ast-global-color-5)}:root .has-ast-global-color-5-background-color{background-color:var(--ast-global-color-5)}:root .wp-block-button .has-ast-global-color-5-color{color:var(--ast-global-color-5)}:root .wp-block-button .has-ast-global-color-5-background-color{background-color:var(--ast-global-color-5)}:root .has-ast-global-color-6-color{color:var(--ast-global-color-6)}:root .has-ast-global-color-6-background-color{background-color:var(--ast-global-color-6)}:root .wp-block-button .has-ast-global-color-6-color{color:var(--ast-global-color-6)}:root .wp-block-button .has-ast-global-color-6-background-color{background-color:var(--ast-global-color-6)}:root .has-ast-global-color-7-color{color:var(--ast-global-color-7)}:root .has-ast-global-color-7-background-color{background-color:var(--ast-global-color-7)}:root .wp-block-button .has-ast-global-color-7-color{color:var(--ast-global-color-7)}:root .wp-block-button .has-ast-global-color-7-background-color{background-color:var(--ast-global-color-7)}:root .has-ast-global-color-8-color{color:var(--ast-global-color-8)}:root .has-ast-global-color-8-background-color{background-color:var(--ast-global-color-8)}:root .wp-block-button .has-ast-global-color-8-color{color:var(--ast-global-color-8)}:root .wp-block-button .has-ast-global-color-8-background-color{background-color:var(--ast-global-color-8)}:root{--ast-global-color-0:#0170B9;--ast-global-color-1:#3a3a3a;--ast-global-color-2:#3a3a3a;--ast-global-color-3:#4B4F58;--ast-global-color-4:#F5F5F5;--ast-global-color-5:#FFFFFF;--ast-global-color-6:#E5E5E5;--ast-global-color-7:#424242;--ast-global-color-8:#000000}:root{--ast-border-color:#75ef71}.site .site-content #primary{margin-top:45px;margin-bottom:0;margin-left:0;margin-right:0}.ast-single-entry-banner{-js-display:flex;display:flex;flex-direction:column;justify-content:center;text-align:center;position:relative;background:#eee}.ast-single-entry-banner[data-banner-layout=layout-1]{max-width:1200px;background:inherit;padding:20px 0}.ast-single-entry-banner[data-banner-width-type=custom]{margin:0 auto;width:100%}.ast-single-entry-banner+.site-content .entry-header{margin-bottom:0}.site .ast-author-avatar{--ast-author-avatar-size: }a.ast-underline-text{text-decoration:underline}.ast-container>.ast-terms-link{position:relative;display:block}a.ast-button.ast-badge-tax{padding:4px 8px;border-radius:3px;font-size:inherit}header.entry-header:not(.related-entry-header) .entry-title{font-size:60px;font-size:3.52941176471rem}header.entry-header:not(.related-entry-header)>*:not(:last-child){margin-bottom:10px}.ast-archive-entry-banner{-js-display:flex;display:flex;flex-direction:column;justify-content:center;text-align:center;position:relative;background:#eee}.ast-archive-entry-banner[data-banner-width-type=custom]{margin:0 auto;width:100%}.ast-archive-entry-banner[data-banner-layout=layout-1]{background:inherit;padding:20px 0;text-align:left}body.archive .ast-archive-description{max-width:1200px;width:100%;text-align:left;padding-top:3em;padding-right:3em;padding-bottom:3em;padding-left:3em}body.archive .ast-archive-description .ast-archive-title,body.archive .ast-archive-description .ast-archive-title *{font-size:60px;font-size:3.52941176471rem;text-transform:capitalize}body.archive .ast-archive-description>*:not(:last-child){margin-bottom:10px}@media(max-width:921px){body.archive .ast-archive-description{text-align:left}body.archive .ast-archive-description .ast-archive-title{font-size:50px;font-size:2.94117647059rem}}@media(max-width:544px){body.archive .ast-archive-description{text-align:left}body.archive .ast-archive-description .ast-archive-title{font-size:30px;font-size:1.76470588235rem}}.ast-breadcrumbs .trail-browse,.ast-breadcrumbs .trail-items,.ast-breadcrumbs .trail-items li{display:inline-block;margin:0;padding:0;border:none;background:inherit;text-indent:0;text-decoration:none}.ast-breadcrumbs .trail-browse{font-size:inherit;font-style:inherit;font-weight:inherit;color:inherit}.ast-breadcrumbs .trail-items{list-style:none}.trail-items li::after{padding:0 .3em;content:"\00bb"}.trail-items li:last-of-type::after{display:none}h1,.entry-content h1,h2,.entry-content h2,h3,.entry-content h3,h4,.entry-content h4,h5,.entry-content h5,h6,.entry-content h6{color:#000}.entry-title a{color:#000}@media(max-width:921px){.ast-builder-grid-row-container.ast-builder-grid-row-tablet-3-firstrow .ast-builder-grid-row>*:first-child,.ast-builder-grid-row-container.ast-builder-grid-row-tablet-3-lastrow .ast-builder-grid-row>*:last-child{grid-column:1/-1}}@media(max-width:544px){.ast-builder-grid-row-container.ast-builder-grid-row-mobile-3-firstrow .ast-builder-grid-row>*:first-child,.ast-builder-grid-row-container.ast-builder-grid-row-mobile-3-lastrow .ast-builder-grid-row>*:last-child{grid-column:1/-1}}.ast-builder-layout-element[data-section=title_tagline]{display:flex}@media(max-width:921px){.ast-header-break-point .ast-builder-layout-element[data-section=title_tagline]{display:flex}}@media(max-width:544px){.ast-header-break-point .ast-builder-layout-element[data-section=title_tagline]{display:flex}}.ast-builder-menu-1{font-family:inherit;font-weight:inherit}.ast-builder-menu-1 .sub-menu,.ast-builder-menu-1 .inline-on-mobile .sub-menu{border-top-width:2px;border-bottom-width:0;border-right-width:0;border-left-width:0;border-color:#cd2653;border-style:solid}.ast-builder-menu-1 .sub-menu .sub-menu{top:-2px}.ast-builder-menu-1 .main-header-menu>.menu-item>.sub-menu,.ast-builder-menu-1 .main-header-menu>.menu-item>.astra-full-megamenu-wrapper{margin-top:0}.ast-desktop .ast-builder-menu-1 .main-header-menu>.menu-item>.sub-menu:before,.ast-desktop .ast-builder-menu-1 .main-header-menu>.menu-item>.astra-full-megamenu-wrapper:before{height:calc( 0px + 2px + 5px )}.ast-desktop .ast-builder-menu-1 .menu-item .sub-menu .menu-link{border-style:none}@media(max-width:921px){.ast-header-break-point .ast-builder-menu-1 .menu-item.menu-item-has-children>.ast-menu-toggle{top:0}.ast-builder-menu-1 .inline-on-mobile .menu-item.menu-item-has-children>.ast-menu-toggle{right:-15px}.ast-builder-menu-1 .menu-item-has-children>.menu-link:after{content:unset}.ast-builder-menu-1 .main-header-menu>.menu-item>.sub-menu,.ast-builder-menu-1 .main-header-menu>.menu-item>.astra-full-megamenu-wrapper{margin-top:0}}@media(max-width:544px){.ast-header-break-point .ast-builder-menu-1 .menu-item.menu-item-has-children>.ast-menu-toggle{top:0}.ast-builder-menu-1 .main-header-menu>.menu-item>.sub-menu,.ast-builder-menu-1 .main-header-menu>.menu-item>.astra-full-megamenu-wrapper{margin-top:0}}.ast-builder-menu-1{display:flex}@media(max-width:921px){.ast-header-break-point .ast-builder-menu-1{display:flex}}@media(max-width:544px){.ast-header-break-point .ast-builder-menu-1{display:flex}}.main-header-bar .main-header-bar-navigation .ast-search-icon{display:block;z-index:4;position:relative}.ast-search-icon .ast-icon{z-index:4}.ast-search-icon{z-index:4;position:relative;line-height:normal}.main-header-bar .ast-search-menu-icon .search-form{background-color:#fff}.ast-search-menu-icon.ast-dropdown-active.slide-search .search-form{visibility:visible;opacity:1}.ast-search-menu-icon .search-form{border:1px solid #e7e7e7;line-height:normal;padding:0 3em 0 0;border-radius:2px;display:inline-block;-webkit-backface-visibility:hidden;backface-visibility:hidden;position:relative;color:inherit;background-color:#fff}.ast-search-menu-icon .astra-search-icon{-js-display:flex;display:flex;line-height:normal}.ast-search-menu-icon .astra-search-icon:focus{outline:none}.ast-search-menu-icon .search-field{border:none;background-color:initial;transition:all .3s;border-radius:inherit;color:inherit;font-size:inherit;width:0;color:#757575}.ast-search-menu-icon .search-submit{display:none;background:0 0;border:none;font-size:1.3em;color:#757575}.ast-search-menu-icon.ast-dropdown-active{visibility:visible;opacity:1;position:relative}.ast-search-menu-icon.ast-dropdown-active .search-field,.ast-dropdown-active.ast-search-menu-icon.slide-search input.search-field{width:235px}.ast-header-search .ast-search-menu-icon.slide-search .search-form,.ast-header-search .ast-search-menu-icon.ast-inline-search .search-form{-js-display:flex;display:flex;align-items:center}.ast-search-menu-icon.ast-inline-search .search-field{width:100%;padding:.6em;padding-right:5.5em;transition:all .2s}.site-header-section-left .ast-search-menu-icon.slide-search .search-form{padding-left:2em;padding-right:unset;left:-1em;right:unset}.site-header-section-left .ast-search-menu-icon.slide-search .search-form .search-field{margin-right:unset}.ast-search-menu-icon.slide-search .search-form{-webkit-backface-visibility:visible;backface-visibility:visible;visibility:hidden;opacity:0;transition:all .2s;position:absolute;z-index:3;right:-1em;top:50%;transform:translateY(-50%)}.ast-header-search .ast-search-menu-icon .search-form .search-field:-ms-input-placeholder,.ast-header-search .ast-search-menu-icon .search-form .search-field:-ms-input-placeholder{opacity:.5}.ast-header-search .ast-search-menu-icon.slide-search .search-form,.ast-header-search .ast-search-menu-icon.ast-inline-search .search-form{-js-display:flex;display:flex;align-items:center}.ast-builder-layout-element.ast-header-search{height:auto}.ast-header-search .astra-search-icon{font-size:18px}@media(max-width:921px){.ast-header-search .astra-search-icon{font-size:40px}}@media(max-width:544px){.ast-header-search .astra-search-icon{font-size:25px}}.ast-header-search{display:flex}@media(max-width:921px){.ast-header-break-point .ast-header-search{display:flex}}@media(max-width:544px){.ast-header-break-point .ast-header-search{display:flex}}.site-below-footer-wrap{padding-top:20px;padding-bottom:20px}.site-below-footer-wrap[data-section=section-below-footer-builder]{background-color:var(--ast-global-color-5);background-image:none;min-height:80px;border-style:solid;border-width:0;border-top-width:1px;border-top-color:var(--ast-global-color-5)}.site-below-footer-wrap[data-section=section-below-footer-builder] .ast-builder-grid-row{max-width:1200px;min-height:80px;margin-left:auto;margin-right:auto}.site-below-footer-wrap[data-section=section-below-footer-builder] .ast-builder-grid-row,.site-below-footer-wrap[data-section=section-below-footer-builder] .site-footer-section{align-items:flex-start}.site-below-footer-wrap[data-section=section-below-footer-builder].ast-footer-row-inline .site-footer-section{display:flex;margin-bottom:0}.ast-builder-grid-row-full .ast-builder-grid-row{grid-template-columns:1fr}@media(max-width:921px){.site-below-footer-wrap[data-section=section-below-footer-builder].ast-footer-row-tablet-inline .site-footer-section{display:flex;margin-bottom:0}.site-below-footer-wrap[data-section=section-below-footer-builder].ast-footer-row-tablet-stack .site-footer-section{display:block;margin-bottom:10px}.ast-builder-grid-row-container.ast-builder-grid-row-tablet-full .ast-builder-grid-row{grid-template-columns:1fr}}@media(max-width:544px){.site-below-footer-wrap[data-section=section-below-footer-builder].ast-footer-row-mobile-inline .site-footer-section{display:flex;margin-bottom:0}.site-below-footer-wrap[data-section=section-below-footer-builder].ast-footer-row-mobile-stack .site-footer-section{display:block;margin-bottom:10px}.ast-builder-grid-row-container.ast-builder-grid-row-mobile-full .ast-builder-grid-row{grid-template-columns:1fr}}.site-below-footer-wrap[data-section=section-below-footer-builder]{display:grid}@media(max-width:921px){.ast-header-break-point .site-below-footer-wrap[data-section=section-below-footer-builder]{display:grid}}@media(max-width:544px){.ast-header-break-point .site-below-footer-wrap[data-section=section-below-footer-builder]{display:grid}}.ast-footer-copyright{text-align:left}.ast-footer-copyright{color:#000}@media(max-width:921px){.ast-footer-copyright{text-align:center}}@media(max-width:544px){.ast-footer-copyright{text-align:left}.ast-footer-copyright{margin-left:10px;margin-right:10px}}.ast-footer-copyright.ast-builder-layout-element{display:flex}@media(max-width:921px){.ast-header-break-point .ast-footer-copyright.ast-builder-layout-element{display:flex}}@media(max-width:544px){.ast-header-break-point .ast-footer-copyright.ast-builder-layout-element{display:flex}}.site-above-footer-wrap{padding-top:20px;padding-bottom:20px}.site-above-footer-wrap[data-section=section-above-footer-builder]{background-color:var(--ast-global-color-5);background-image:none;min-height:60px}.site-above-footer-wrap[data-section=section-above-footer-builder] .ast-builder-grid-row{max-width:1200px;min-height:60px;margin-left:auto;margin-right:auto}.site-above-footer-wrap[data-section=section-above-footer-builder] .ast-builder-grid-row,.site-above-footer-wrap[data-section=section-above-footer-builder] .site-footer-section{align-items:flex-start}.site-above-footer-wrap[data-section=section-above-footer-builder].ast-footer-row-inline .site-footer-section{display:flex;margin-bottom:0}.ast-builder-grid-row-2-equal .ast-builder-grid-row{grid-template-columns:repeat( 2,1fr )}@media(max-width:921px){.site-above-footer-wrap[data-section=section-above-footer-builder].ast-footer-row-tablet-inline .site-footer-section{display:flex;margin-bottom:0}.site-above-footer-wrap[data-section=section-above-footer-builder].ast-footer-row-tablet-stack .site-footer-section{display:block;margin-bottom:10px}.ast-builder-grid-row-container.ast-builder-grid-row-tablet-2-equal .ast-builder-grid-row{grid-template-columns:repeat( 2,1fr )}}@media(max-width:544px){.site-above-footer-wrap[data-section=section-above-footer-builder].ast-footer-row-mobile-inline .site-footer-section{display:flex;margin-bottom:0}.site-above-footer-wrap[data-section=section-above-footer-builder].ast-footer-row-mobile-stack .site-footer-section{display:block;margin-bottom:10px}.ast-builder-grid-row-container.ast-builder-grid-row-mobile-full .ast-builder-grid-row{grid-template-columns:1fr}}.site-above-footer-wrap[data-section=section-above-footer-builder]{padding-top:40px}@media(max-width:544px){.site-above-footer-wrap[data-section=section-above-footer-builder]{margin-left:10px;margin-right:10px}}.site-above-footer-wrap[data-section=section-above-footer-builder]{display:grid}@media(max-width:921px){.ast-header-break-point .site-above-footer-wrap[data-section=section-above-footer-builder]{display:grid}}@media(max-width:544px){.ast-header-break-point .site-above-footer-wrap[data-section=section-above-footer-builder]{display:none}}.site-footer{background-color:#fff;background-image:none}.site-primary-footer-wrap{padding-top:45px;padding-bottom:45px}.site-primary-footer-wrap[data-section=section-primary-footer-builder]{background-color:var(--ast-global-color-5);background-image:none;border-style:solid;border-width:0;border-top-width:1px;border-top-color:var(--ast-global-color-5)}.site-primary-footer-wrap[data-section=section-primary-footer-builder] .ast-builder-grid-row{max-width:1200px;margin-left:auto;margin-right:auto}.site-primary-footer-wrap[data-section=section-primary-footer-builder] .ast-builder-grid-row,.site-primary-footer-wrap[data-section=section-primary-footer-builder] .site-footer-section{align-items:flex-start}.site-primary-footer-wrap[data-section=section-primary-footer-builder].ast-footer-row-inline .site-footer-section{display:flex;margin-bottom:0}.ast-builder-grid-row-full .ast-builder-grid-row{grid-template-columns:1fr}@media(max-width:921px){.site-primary-footer-wrap[data-section=section-primary-footer-builder].ast-footer-row-tablet-inline .site-footer-section{display:flex;margin-bottom:0}.site-primary-footer-wrap[data-section=section-primary-footer-builder].ast-footer-row-tablet-stack .site-footer-section{display:block;margin-bottom:10px}.ast-builder-grid-row-container.ast-builder-grid-row-tablet-full .ast-builder-grid-row{grid-template-columns:1fr}}@media(max-width:544px){.site-primary-footer-wrap[data-section=section-primary-footer-builder].ast-footer-row-mobile-inline .site-footer-section{display:flex;margin-bottom:0}.site-primary-footer-wrap[data-section=section-primary-footer-builder].ast-footer-row-mobile-stack .site-footer-section{display:block;margin-bottom:10px}.ast-builder-grid-row-container.ast-builder-grid-row-mobile-full .ast-builder-grid-row{grid-template-columns:1fr}}.site-primary-footer-wrap[data-section=section-primary-footer-builder]{display:grid}@media(max-width:921px){.ast-header-break-point .site-primary-footer-wrap[data-section=section-primary-footer-builder]{display:grid}}@media(max-width:544px){.ast-header-break-point .site-primary-footer-wrap[data-section=section-primary-footer-builder]{display:grid}}.footer-widget-area[data-section=sidebar-widgets-footer-widget-1].footer-widget-area-inner{text-align:left}@media(max-width:921px){.footer-widget-area[data-section=sidebar-widgets-footer-widget-1].footer-widget-area-inner{text-align:center}}@media(max-width:544px){.footer-widget-area[data-section=sidebar-widgets-footer-widget-1].footer-widget-area-inner{text-align:center}}.footer-widget-area[data-section=sidebar-widgets-footer-widget-3].footer-widget-area-inner{text-align:left}@media(max-width:921px){.footer-widget-area[data-section=sidebar-widgets-footer-widget-3].footer-widget-area-inner{text-align:center}}@media(max-width:544px){.footer-widget-area[data-section=sidebar-widgets-footer-widget-3].footer-widget-area-inner{text-align:center}}.footer-widget-area.widget-area.site-footer-focus-item{width:auto}.ast-footer-row-inline .footer-widget-area.widget-area.site-footer-focus-item{width:100%}.footer-widget-area[data-section=sidebar-widgets-footer-widget-1]{display:block}@media(max-width:921px){.ast-header-break-point .footer-widget-area[data-section=sidebar-widgets-footer-widget-1]{display:block}}@media(max-width:544px){.ast-header-break-point .footer-widget-area[data-section=sidebar-widgets-footer-widget-1]{display:block}}.footer-widget-area[data-section=sidebar-widgets-footer-widget-3]{display:block}@media(max-width:921px){.ast-header-break-point .footer-widget-area[data-section=sidebar-widgets-footer-widget-3]{display:block}}@media(max-width:544px){.ast-header-break-point .footer-widget-area[data-section=sidebar-widgets-footer-widget-3]{display:block}}.ast-header-break-point .main-header-bar{border-bottom-width:1px}@media(min-width:922px){.main-header-bar{border-bottom-width:1px}}.main-header-menu .menu-item,#astra-footer-menu .menu-item,.main-header-bar .ast-masthead-custom-menu-items{-js-display:flex;display:flex;-webkit-box-pack:center;-webkit-justify-content:center;-moz-box-pack:center;-ms-flex-pack:center;justify-content:center;-webkit-box-orient:vertical;-webkit-box-direction:normal;-webkit-flex-direction:column;-moz-box-orient:vertical;-moz-box-direction:normal;-ms-flex-direction:column;flex-direction:column}.main-header-menu>.menu-item>.menu-link,#astra-footer-menu>.menu-item>.menu-link{height:100%;-webkit-box-align:center;-webkit-align-items:center;-moz-box-align:center;-ms-flex-align:center;align-items:center;-js-display:flex;display:flex}.ast-header-break-point .main-navigation ul .menu-item .menu-link .icon-arrow:first-of-type svg{top:.2em;margin-top:0;margin-left:0;width:.65em;transform:translate(0,-2px)rotateZ(270deg)}.ast-mobile-popup-content .ast-submenu-expanded>.ast-menu-toggle{transform:rotateX(180deg);overflow-y:auto}@media(min-width:922px){.ast-builder-menu .main-navigation>ul>li:last-child a{margin-right:0}}.ast-separate-container .ast-article-inner{background-color:initial;background-image:none}.ast-separate-container .ast-article-post{background-color:#f6fef6;background-image:none}@media(max-width:921px){.ast-separate-container .ast-article-post{background-color:#f6fef6;background-image:none}}@media(max-width:544px){.ast-separate-container .ast-article-post{background-color:#f6fef6;background-image:none}}.ast-separate-container .ast-article-single:not(.ast-related-post),.woocommerce.ast-separate-container .ast-woocommerce-container,.ast-separate-container .error-404,.ast-separate-container .no-results,.single.ast-separate-container .site-main .ast-author-meta,.ast-separate-container .related-posts-title-wrapper,.ast-separate-container .comments-count-wrapper,.ast-box-layout.ast-plain-container .site-content,.ast-padded-layout.ast-plain-container .site-content,.ast-separate-container .ast-archive-description,.ast-separate-container .comments-area .comment-respond,.ast-separate-container .comments-area .ast-comment-list li,.ast-separate-container .comments-area .comments-title{background-color:#f6fef6;background-image:none}@media(max-width:921px){.ast-separate-container .ast-article-single:not(.ast-related-post),.woocommerce.ast-separate-container .ast-woocommerce-container,.ast-separate-container .error-404,.ast-separate-container .no-results,.single.ast-separate-container .site-main .ast-author-meta,.ast-separate-container .related-posts-title-wrapper,.ast-separate-container .comments-count-wrapper,.ast-box-layout.ast-plain-container .site-content,.ast-padded-layout.ast-plain-container .site-content,.ast-separate-container .ast-archive-description{background-color:#f6fef6;background-image:none}}@media(max-width:544px){.ast-separate-container .ast-article-single:not(.ast-related-post),.woocommerce.ast-separate-container .ast-woocommerce-container,.ast-separate-container .error-404,.ast-separate-container .no-results,.single.ast-separate-container .site-main .ast-author-meta,.ast-separate-container .related-posts-title-wrapper,.ast-separate-container .comments-count-wrapper,.ast-box-layout.ast-plain-container .site-content,.ast-padded-layout.ast-plain-container .site-content,.ast-separate-container .ast-archive-description{background-color:#f6fef6;background-image:none}}.ast-separate-container.ast-two-container #secondary .widget{background-color:#f6fef6;background-image:none}@media(max-width:921px){.ast-separate-container.ast-two-container #secondary .widget{background-color:#f6fef6;background-image:none}}@media(max-width:544px){.ast-separate-container.ast-two-container #secondary .widget{background-color:#f6fef6;background-image:none}}.ast-plain-container,.ast-page-builder-template{background-color:#f6fef6;background-image:none}@media(max-width:921px){.ast-plain-container,.ast-page-builder-template{background-color:#f6fef6;background-image:none}}@media(max-width:544px){.ast-plain-container,.ast-page-builder-template{background-color:#f6fef6;background-image:none}}.ast-related-post-title,.entry-meta *{word-break:break-word}.ast-related-post-cta.read-more .ast-related-post-link{text-decoration:none}.ast-page-builder-template .ast-related-post .entry-header,.ast-related-post-content .entry-header,.ast-related-post-content .entry-meta{margin:1em auto;padding:0}.ast-related-posts-wrapper{display:grid;grid-column-gap:25px;grid-row-gap:25px}.ast-related-posts-wrapper .ast-related-post,.ast-related-post-featured-section{padding:0;margin:0;width:100%;position:relative}.ast-related-posts-inner-section{height:100%}.post-has-thumb+.entry-header,.post-has-thumb+.entry-content{margin-top:1em}.ast-related-post-content .entry-meta{margin-top:.5em}.ast-related-posts-inner-section .post-thumb-img-content{margin:0;position:relative}.ast-single-related-posts-container{border-top:1px solid var(--ast-single-post-border,var(--ast-border-color))}.ast-separate-container .ast-single-related-posts-container{border-top:0}.ast-single-related-posts-container{padding-top:2em}.ast-related-posts-title-section{padding-bottom:2em}.ast-page-builder-template .ast-single-related-posts-container{margin-top:0;padding-left:20px;padding-right:20px}@media(max-width:544px){.ast-related-posts-title-section{padding-bottom:1.5em}}.ast-single-related-posts-container .ast-related-posts-wrapper{grid-template-columns:repeat( 2,1fr )}.ast-related-posts-inner-section .ast-date-meta .posted-on,.ast-related-posts-inner-section .ast-date-meta .posted-on *{background:#cd2653;color:#fff}.ast-related-posts-inner-section .ast-date-meta .posted-on .date-month,.ast-related-posts-inner-section .ast-date-meta .posted-on .date-year{color:#fff}.ast-single-related-posts-container{background-color:#fff}.ast-related-posts-title{font-size:30px;font-size:1.76470588235rem;line-height:1.6em}.ast-related-posts-title-section .ast-related-posts-title{text-align:left}.ast-related-post-content .entry-header .ast-related-post-title,.ast-related-post-content .entry-header .ast-related-post-title a{font-size:20px;font-size:1.17647058824rem;line-height:1em}.ast-related-post-content .entry-meta,.ast-related-post-content .entry-meta *{font-size:14px;font-size:.823529411765rem;line-height:1.6em}.ast-related-cat-style--badge .cat-links>a,.ast-related-tag-style--badge .tags-links>a{border-style:solid;border-top-width:0;border-right-width:0;border-left-width:0;border-bottom-width:0;padding:4px 8px;border-radius:3px;font-size:inherit;color:var(--ast-global-color-5);border-color:rgba(204,39,83,.48);background-color:rgba(204,39,83,.48)}.ast-related-cat-style--badge .cat-links>a:hover,.ast-related-tag-style--badge .tags-links>a:hover{color:var(--ast-global-color-5);background-color:#cd2653;border-color:#cd2653}.ast-related-cat-style--underline .cat-links>a,.ast-related-tag-style--underline .tags-links>a{text-decoration:underline}@media(max-width:921px){.ast-single-related-posts-container .ast-related-posts-wrapper .ast-related-post{width:100%}.ast-single-related-posts-container .ast-related-posts-wrapper{grid-template-columns:repeat( 2,1fr )}.ast-single-related-posts-container{background-color:#fff}}@media(max-width:544px){.ast-single-related-posts-container .ast-related-posts-wrapper{grid-template-columns:1fr}.ast-single-related-posts-container{background-color:#fff}}.site .ast-single-related-posts-container{padding-top:2.5em;padding-bottom:2.5em;padding-left:2.5em;padding-right:2.5em;margin-top:2em}.ast-mobile-header-content>*,.ast-desktop-header-content>*{padding:10px 0;height:auto}.ast-mobile-header-content>*:first-child,.ast-desktop-header-content>*:first-child{padding-top:10px}.ast-mobile-header-content>.ast-builder-menu,.ast-desktop-header-content>.ast-builder-menu{padding-top:0}.ast-mobile-header-content>*:last-child,.ast-desktop-header-content>*:last-child{padding-bottom:0}.ast-mobile-header-content .ast-search-menu-icon.ast-inline-search label,.ast-desktop-header-content .ast-search-menu-icon.ast-inline-search label{width:100%}.ast-desktop-header-content .main-header-bar-navigation .ast-submenu-expanded>.ast-menu-toggle::before{transform:rotateX(180deg)}#ast-desktop-header .ast-desktop-header-content,.ast-mobile-header-content .ast-search-icon,.ast-desktop-header-content .ast-search-icon,.ast-mobile-header-wrap .ast-mobile-header-content,.ast-main-header-nav-open.ast-popup-nav-open .ast-mobile-header-wrap .ast-mobile-header-content,.ast-main-header-nav-open.ast-popup-nav-open .ast-desktop-header-content{display:none}.ast-main-header-nav-open.ast-header-break-point #ast-desktop-header .ast-desktop-header-content,.ast-main-header-nav-open.ast-header-break-point .ast-mobile-header-wrap .ast-mobile-header-content{display:block}.ast-desktop .ast-desktop-header-content .astra-menu-animation-slide-up>.menu-item>.sub-menu,.ast-desktop .ast-desktop-header-content .astra-menu-animation-slide-up>.menu-item .menu-item>.sub-menu,.ast-desktop .ast-desktop-header-content .astra-menu-animation-slide-down>.menu-item>.sub-menu,.ast-desktop .ast-desktop-header-content .astra-menu-animation-slide-down>.menu-item .menu-item>.sub-menu,.ast-desktop .ast-desktop-header-content .astra-menu-animation-fade>.menu-item>.sub-menu,.ast-desktop .ast-desktop-header-content .astra-menu-animation-fade>.menu-item .menu-item>.sub-menu{opacity:1;visibility:visible}.ast-hfb-header.ast-default-menu-enable.ast-header-break-point .ast-mobile-header-wrap .ast-mobile-header-content .main-header-bar-navigation{width:unset;margin:unset}.ast-mobile-header-content.content-align-flex-end .main-header-bar-navigation .menu-item-has-children>.ast-menu-toggle,.ast-desktop-header-content.content-align-flex-end .main-header-bar-navigation .menu-item-has-children>.ast-menu-toggle{left:calc( 20px - .907em);right:auto}.ast-mobile-header-content .ast-search-menu-icon,.ast-mobile-header-content .ast-search-menu-icon.slide-search,.ast-desktop-header-content .ast-search-menu-icon,.ast-desktop-header-content .ast-search-menu-icon.slide-search{width:100%;position:relative;display:block;right:auto;transform:none}.ast-mobile-header-content .ast-search-menu-icon.slide-search .search-form,.ast-mobile-header-content .ast-search-menu-icon .search-form,.ast-desktop-header-content .ast-search-menu-icon.slide-search .search-form,.ast-desktop-header-content .ast-search-menu-icon .search-form{right:0;visibility:visible;opacity:1;position:relative;top:auto;transform:none;padding:0;display:block;overflow:hidden}.ast-mobile-header-content .ast-search-menu-icon.ast-inline-search .search-field,.ast-mobile-header-content .ast-search-menu-icon .search-field,.ast-desktop-header-content .ast-search-menu-icon.ast-inline-search .search-field,.ast-desktop-header-content .ast-search-menu-icon .search-field{width:100%;padding-right:5.5em}.ast-mobile-header-content .ast-search-menu-icon .search-submit,.ast-desktop-header-content .ast-search-menu-icon .search-submit{display:block;position:absolute;height:100%;top:0;right:0;padding:0 1em;border-radius:0}.ast-hfb-header.ast-default-menu-enable.ast-header-break-point .ast-mobile-header-wrap .ast-mobile-header-content .main-header-bar-navigation ul .sub-menu .menu-link{padding-left:30px}.ast-hfb-header.ast-default-menu-enable.ast-header-break-point .ast-mobile-header-wrap .ast-mobile-header-content .main-header-bar-navigation .sub-menu .menu-item .menu-item .menu-link{padding-left:40px}.ast-mobile-popup-drawer.active .ast-mobile-popup-inner{background-color:#fff}.ast-mobile-header-wrap .ast-mobile-header-content,.ast-desktop-header-content{background-color:#fff}.ast-mobile-popup-content>*,.ast-mobile-header-content>*,.ast-desktop-popup-content>*,.ast-desktop-header-content>*{padding-top:0;padding-bottom:0}.content-align-flex-start .ast-builder-layout-element{justify-content:flex-start}.content-align-flex-start .main-header-menu{text-align:left}.ast-mobile-popup-drawer.active .menu-toggle-close{color:#3a3a3a}.ast-mobile-header-wrap .ast-primary-header-bar,.ast-primary-header-bar .site-primary-header-wrap{min-height:80px}.ast-desktop .ast-primary-header-bar .main-header-menu>.menu-item{line-height:80px}.ast-header-break-point #masthead .ast-mobile-header-wrap .ast-primary-header-bar,.ast-header-break-point #masthead .ast-mobile-header-wrap .ast-below-header-bar,.ast-header-break-point #masthead .ast-mobile-header-wrap .ast-above-header-bar{padding-left:20px;padding-right:20px}.ast-header-break-point .ast-primary-header-bar{border-bottom-width:1px;border-bottom-color:#eaeaea;border-bottom-style:solid}@media(min-width:922px){.ast-primary-header-bar{border-bottom-width:1px;border-bottom-color:#eaeaea;border-bottom-style:solid}}.ast-primary-header-bar{background-color:#fff}.ast-primary-header-bar{display:block}@media(max-width:921px){.ast-header-break-point .ast-primary-header-bar{display:grid}}@media(max-width:544px){.ast-header-break-point .ast-primary-header-bar{display:grid}}[data-section=section-header-mobile-trigger] .ast-button-wrap .ast-mobile-menu-trigger-outline{background:0 0;color:#cd2653;border-top-width:1px;border-bottom-width:1px;border-right-width:1px;border-left-width:1px;border-style:solid;border-color:#cd2653}[data-section=section-header-mobile-trigger] .ast-button-wrap .mobile-menu-toggle-icon .ast-mobile-svg{width:25px;height:25px;fill:#cd2653}[data-section=section-header-mobile-trigger] .ast-button-wrap .mobile-menu-wrap .mobile-menu{color:#cd2653}.ast-builder-menu-mobile .main-navigation .menu-item.menu-item-has-children>.ast-menu-toggle{top:0}.ast-builder-menu-mobile .main-navigation .menu-item-has-children>.menu-link:after{content:unset}.ast-hfb-header .ast-builder-menu-mobile .main-header-menu,.ast-hfb-header .ast-builder-menu-mobile .main-navigation .menu-item .menu-link,.ast-hfb-header .ast-builder-menu-mobile .main-navigation .menu-item .sub-menu .menu-link{border-style:none}.ast-builder-menu-mobile .main-navigation .menu-item.menu-item-has-children>.ast-menu-toggle{top:0}@media(max-width:921px){.ast-builder-menu-mobile .main-navigation .menu-item.menu-item-has-children>.ast-menu-toggle{top:0}.ast-builder-menu-mobile .main-navigation .menu-item-has-children>.menu-link:after{content:unset}}@media(max-width:544px){.ast-builder-menu-mobile .main-navigation .menu-item.menu-item-has-children>.ast-menu-toggle{top:0}}.ast-builder-menu-mobile .main-navigation{display:block}@media(max-width:921px){.ast-header-break-point .ast-builder-menu-mobile .main-navigation{display:block}}@media(max-width:544px){.ast-header-break-point .ast-builder-menu-mobile .main-navigation{display:block}}.footer-nav-wrap .astra-footer-vertical-menu{display:grid}@media(min-width:769px){.footer-nav-wrap .astra-footer-horizontal-menu li{margin:0}.footer-nav-wrap .astra-footer-horizontal-menu a{padding:0 .5em}}@media(min-width:769px){.footer-nav-wrap .astra-footer-horizontal-menu li:first-child a{padding-left:0}.footer-nav-wrap .astra-footer-horizontal-menu li:last-child a{padding-right:0}}.footer-widget-area[data-section=section-footer-menu] .astra-footer-horizontal-menu{justify-content:center}.footer-widget-area[data-section=section-footer-menu] .astra-footer-vertical-menu .menu-item{align-items:center}@media(max-width:921px){.footer-widget-area[data-section=section-footer-menu] .astra-footer-tablet-horizontal-menu{justify-content:flex-start;display:flex}.footer-widget-area[data-section=section-footer-menu] .astra-footer-tablet-vertical-menu{display:grid;justify-content:flex-start}.footer-widget-area[data-section=section-footer-menu] .astra-footer-tablet-vertical-menu .menu-item{align-items:flex-start}#astra-footer-menu .menu-item>a{padding-top:0;padding-bottom:0;padding-left:0;padding-right:0}}@media(max-width:544px){#astra-footer-menu{margin-top:0;margin-bottom:0;margin-left:10px;margin-right:10px}.footer-widget-area[data-section=section-footer-menu] .astra-footer-mobile-horizontal-menu{justify-content:center;display:flex}.footer-widget-area[data-section=section-footer-menu] .astra-footer-mobile-vertical-menu{display:grid;justify-content:center}.footer-widget-area[data-section=section-footer-menu] .astra-footer-mobile-vertical-menu .menu-item{align-items:center}#astra-footer-menu .menu-item>a{padding-left:2px;padding-right:0}}.footer-widget-area[data-section=section-footer-menu]{display:block}@media(max-width:921px){.ast-header-break-point .footer-widget-area[data-section=section-footer-menu]{display:block}}@media(max-width:544px){.ast-header-break-point .footer-widget-area[data-section=section-footer-menu]{display:block}}</style><link rel=stylesheet id=astra-google-fonts-css href="https://fonts.googleapis.com/css?display=swap&family=Karla%3A400%7CRubik%3A600%2C500&ver=4.8.12" media=all><style id=wp-emoji-styles-inline-css>img.wp-smiley,img.emoji{display:inline!important;border:none!important;box-shadow:0 0!important;height:1em!important;width:1em!important;margin:0 .07em!important;vertical-align:-.1em!important;background:0 0!important;padding:0!important}</style><link rel=stylesheet id=wp-block-library-css href="https://123mathe.de/wp-includes/css/dist/block-library/style.min.css?ezmin=true&ff=1&ver=6.7.2&wps=false" media=all><style id=global-styles-inline-css>:root{--wp--preset--aspect-ratio--square:1;--wp--preset--aspect-ratio--4-3:4/3;--wp--preset--aspect-ratio--3-4:3/4;--wp--preset--aspect-ratio--3-2:3/2;--wp--preset--aspect-ratio--2-3:2/3;--wp--preset--aspect-ratio--16-9:16/9;--wp--preset--aspect-ratio--9-16:9/16;--wp--preset--color--black:#000000;--wp--preset--color--cyan-bluish-gray:#abb8c3;--wp--preset--color--white:#ffffff;--wp--preset--color--pale-pink:#f78da7;--wp--preset--color--vivid-red:#cf2e2e;--wp--preset--color--luminous-vivid-orange:#ff6900;--wp--preset--color--luminous-vivid-amber:#fcb900;--wp--preset--color--light-green-cyan:#7bdcb5;--wp--preset--color--vivid-green-cyan:#00d084;--wp--preset--color--pale-cyan-blue:#8ed1fc;--wp--preset--color--vivid-cyan-blue:#0693e3;--wp--preset--color--vivid-purple:#9b51e0;--wp--preset--color--ast-global-color-0:var(--ast-global-color-0);--wp--preset--color--ast-global-color-1:var(--ast-global-color-1);--wp--preset--color--ast-global-color-2:var(--ast-global-color-2);--wp--preset--color--ast-global-color-3:var(--ast-global-color-3);--wp--preset--color--ast-global-color-4:var(--ast-global-color-4);--wp--preset--color--ast-global-color-5:var(--ast-global-color-5);--wp--preset--color--ast-global-color-6:var(--ast-global-color-6);--wp--preset--color--ast-global-color-7:var(--ast-global-color-7);--wp--preset--color--ast-global-color-8:var(--ast-global-color-8);--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple:linear-gradient(135deg,rgba(6,147,227,1) 0%,rgb(155,81,224) 100%);--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan:linear-gradient(135deg,rgb(122,220,180) 0%,rgb(0,208,130) 100%);--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange:linear-gradient(135deg,rgba(252,185,0,1) 0%,rgba(255,105,0,1) 100%);--wp--preset--gradient--luminous-vivid-orange-to-vivid-red:linear-gradient(135deg,rgba(255,105,0,1) 0%,rgb(207,46,46) 100%);--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(169,184,195) 100%);--wp--preset--gradient--cool-to-warm-spectrum:linear-gradient(135deg,rgb(74,234,220) 0%,rgb(151,120,209) 20%,rgb(207,42,186) 40%,rgb(238,44,130) 60%,rgb(251,105,98) 80%,rgb(254,248,76) 100%);--wp--preset--gradient--blush-light-purple:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(152,150,240) 100%);--wp--preset--gradient--blush-bordeaux:linear-gradient(135deg,rgb(254,205,165) 0%,rgb(254,45,45) 50%,rgb(107,0,62) 100%);--wp--preset--gradient--luminous-dusk:linear-gradient(135deg,rgb(255,203,112) 0%,rgb(199,81,192) 50%,rgb(65,88,208) 100%);--wp--preset--gradient--pale-ocean:linear-gradient(135deg,rgb(255,245,203) 0%,rgb(182,227,212) 50%,rgb(51,167,181) 100%);--wp--preset--gradient--electric-grass:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(113,206,126) 100%);--wp--preset--gradient--midnight:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(40,116,252) 100%);--wp--preset--font-size--small:13px;--wp--preset--font-size--medium:20px;--wp--preset--font-size--large:36px;--wp--preset--font-size--x-large:42px;--wp--preset--spacing--20:0.44rem;--wp--preset--spacing--30:0.67rem;--wp--preset--spacing--40:1rem;--wp--preset--spacing--50:1.5rem;--wp--preset--spacing--60:2.25rem;--wp--preset--spacing--70:3.38rem;--wp--preset--spacing--80:5.06rem;--wp--preset--shadow--natural:6px 6px 9px rgba(0, 0, 0, 0.2);--wp--preset--shadow--deep:12px 12px 50px rgba(0, 0, 0, 0.4);--wp--preset--shadow--sharp:6px 6px 0px rgba(0, 0, 0, 0.2);--wp--preset--shadow--outlined:6px 6px 0px -3px rgba(255, 255, 255, 1), 6px 6px rgba(0, 0, 0, 1);--wp--preset--shadow--crisp:6px 6px 0px rgba(0, 0, 0, 1)}:root{--wp--style--global--content-size:var(--wp--custom--ast-content-width-size);--wp--style--global--wide-size:var(--wp--custom--ast-wide-width-size)}:where(body){margin:0}.wp-site-blocks>.alignleft{float:left;margin-right:2em}.wp-site-blocks>.alignright{float:right;margin-left:2em}.wp-site-blocks>.aligncenter{justify-content:center;margin-left:auto;margin-right:auto}:where(.wp-site-blocks)>*{margin-block-start:24px;margin-block-end:0}:where(.wp-site-blocks)>:first-child{margin-block-start:0}:where(.wp-site-blocks)>:last-child{margin-block-end:0}:root{--wp--style--block-gap:24px}:root :where(.is-layout-flow)>:first-child{margin-block-start:0}:root :where(.is-layout-flow)>:last-child{margin-block-end:0}:root :where(.is-layout-flow)>*{margin-block-start:24px;margin-block-end:0}:root :where(.is-layout-constrained)>:first-child{margin-block-start:0}:root :where(.is-layout-constrained)>:last-child{margin-block-end:0}:root :where(.is-layout-constrained)>*{margin-block-start:24px;margin-block-end:0}:root :where(.is-layout-flex){gap:24px}:root :where(.is-layout-grid){gap:24px}.is-layout-flow>.alignleft{float:left;margin-inline-start:0;margin-inline-end:2em}.is-layout-flow>.alignright{float:right;margin-inline-start:2em;margin-inline-end:0}.is-layout-flow>.aligncenter{margin-left:auto!important;margin-right:auto!important}.is-layout-constrained>.alignleft{float:left;margin-inline-start:0;margin-inline-end:2em}.is-layout-constrained>.alignright{float:right;margin-inline-start:2em;margin-inline-end:0}.is-layout-constrained>.aligncenter{margin-left:auto!important;margin-right:auto!important}.is-layout-constrained>:where(:not(.alignleft):not(.alignright):not(.alignfull)){max-width:var(--wp--style--global--content-size);margin-left:auto!important;margin-right:auto!important}.is-layout-constrained>.alignwide{max-width:var(--wp--style--global--wide-size)}body .is-layout-flex{display:flex}.is-layout-flex{flex-wrap:wrap;align-items:center}.is-layout-flex>:is(*,div){margin:0}body .is-layout-grid{display:grid}.is-layout-grid>:is(*,div){margin:0}body{padding-top:0;padding-right:0;padding-bottom:0;padding-left:0}a:where(:not(.wp-element-button)){text-decoration:none}:root :where(.wp-element-button,.wp-block-button__link){background-color:#32373c;border-width:0;color:#fff;font-family:inherit;font-size:inherit;line-height:inherit;padding:calc(.667em + 2px)calc(1.333em + 2px);text-decoration:none}.has-black-color{color:var(--wp--preset--color--black)!important}.has-cyan-bluish-gray-color{color:var(--wp--preset--color--cyan-bluish-gray)!important}.has-white-color{color:var(--wp--preset--color--white)!important}.has-pale-pink-color{color:var(--wp--preset--color--pale-pink)!important}.has-vivid-red-color{color:var(--wp--preset--color--vivid-red)!important}.has-luminous-vivid-orange-color{color:var(--wp--preset--color--luminous-vivid-orange)!important}.has-luminous-vivid-amber-color{color:var(--wp--preset--color--luminous-vivid-amber)!important}.has-light-green-cyan-color{color:var(--wp--preset--color--light-green-cyan)!important}.has-vivid-green-cyan-color{color:var(--wp--preset--color--vivid-green-cyan)!important}.has-pale-cyan-blue-color{color:var(--wp--preset--color--pale-cyan-blue)!important}.has-vivid-cyan-blue-color{color:var(--wp--preset--color--vivid-cyan-blue)!important}.has-vivid-purple-color{color:var(--wp--preset--color--vivid-purple)!important}.has-ast-global-color-0-color{color:var(--wp--preset--color--ast-global-color-0)!important}.has-ast-global-color-1-color{color:var(--wp--preset--color--ast-global-color-1)!important}.has-ast-global-color-2-color{color:var(--wp--preset--color--ast-global-color-2)!important}.has-ast-global-color-3-color{color:var(--wp--preset--color--ast-global-color-3)!important}.has-ast-global-color-4-color{color:var(--wp--preset--color--ast-global-color-4)!important}.has-ast-global-color-5-color{color:var(--wp--preset--color--ast-global-color-5)!important}.has-ast-global-color-6-color{color:var(--wp--preset--color--ast-global-color-6)!important}.has-ast-global-color-7-color{color:var(--wp--preset--color--ast-global-color-7)!important}.has-ast-global-color-8-color{color:var(--wp--preset--color--ast-global-color-8)!important}.has-black-background-color{background-color:var(--wp--preset--color--black)!important}.has-cyan-bluish-gray-background-color{background-color:var(--wp--preset--color--cyan-bluish-gray)!important}.has-white-background-color{background-color:var(--wp--preset--color--white)!important}.has-pale-pink-background-color{background-color:var(--wp--preset--color--pale-pink)!important}.has-vivid-red-background-color{background-color:var(--wp--preset--color--vivid-red)!important}.has-luminous-vivid-orange-background-color{background-color:var(--wp--preset--color--luminous-vivid-orange)!important}.has-luminous-vivid-amber-background-color{background-color:var(--wp--preset--color--luminous-vivid-amber)!important}.has-light-green-cyan-background-color{background-color:var(--wp--preset--color--light-green-cyan)!important}.has-vivid-green-cyan-background-color{background-color:var(--wp--preset--color--vivid-green-cyan)!important}.has-pale-cyan-blue-background-color{background-color:var(--wp--preset--color--pale-cyan-blue)!important}.has-vivid-cyan-blue-background-color{background-color:var(--wp--preset--color--vivid-cyan-blue)!important}.has-vivid-purple-background-color{background-color:var(--wp--preset--color--vivid-purple)!important}.has-ast-global-color-0-background-color{background-color:var(--wp--preset--color--ast-global-color-0)!important}.has-ast-global-color-1-background-color{background-color:var(--wp--preset--color--ast-global-color-1)!important}.has-ast-global-color-2-background-color{background-color:var(--wp--preset--color--ast-global-color-2)!important}.has-ast-global-color-3-background-color{background-color:var(--wp--preset--color--ast-global-color-3)!important}.has-ast-global-color-4-background-color{background-color:var(--wp--preset--color--ast-global-color-4)!important}.has-ast-global-color-5-background-color{background-color:var(--wp--preset--color--ast-global-color-5)!important}.has-ast-global-color-6-background-color{background-color:var(--wp--preset--color--ast-global-color-6)!important}.has-ast-global-color-7-background-color{background-color:var(--wp--preset--color--ast-global-color-7)!important}.has-ast-global-color-8-background-color{background-color:var(--wp--preset--color--ast-global-color-8)!important}.has-black-border-color{border-color:var(--wp--preset--color--black)!important}.has-cyan-bluish-gray-border-color{border-color:var(--wp--preset--color--cyan-bluish-gray)!important}.has-white-border-color{border-color:var(--wp--preset--color--white)!important}.has-pale-pink-border-color{border-color:var(--wp--preset--color--pale-pink)!important}.has-vivid-red-border-color{border-color:var(--wp--preset--color--vivid-red)!important}.has-luminous-vivid-orange-border-color{border-color:var(--wp--preset--color--luminous-vivid-orange)!important}.has-luminous-vivid-amber-border-color{border-color:var(--wp--preset--color--luminous-vivid-amber)!important}.has-light-green-cyan-border-color{border-color:var(--wp--preset--color--light-green-cyan)!important}.has-vivid-green-cyan-border-color{border-color:var(--wp--preset--color--vivid-green-cyan)!important}.has-pale-cyan-blue-border-color{border-color:var(--wp--preset--color--pale-cyan-blue)!important}.has-vivid-cyan-blue-border-color{border-color:var(--wp--preset--color--vivid-cyan-blue)!important}.has-vivid-purple-border-color{border-color:var(--wp--preset--color--vivid-purple)!important}.has-ast-global-color-0-border-color{border-color:var(--wp--preset--color--ast-global-color-0)!important}.has-ast-global-color-1-border-color{border-color:var(--wp--preset--color--ast-global-color-1)!important}.has-ast-global-color-2-border-color{border-color:var(--wp--preset--color--ast-global-color-2)!important}.has-ast-global-color-3-border-color{border-color:var(--wp--preset--color--ast-global-color-3)!important}.has-ast-global-color-4-border-color{border-color:var(--wp--preset--color--ast-global-color-4)!important}.has-ast-global-color-5-border-color{border-color:var(--wp--preset--color--ast-global-color-5)!important}.has-ast-global-color-6-border-color{border-color:var(--wp--preset--color--ast-global-color-6)!important}.has-ast-global-color-7-border-color{border-color:var(--wp--preset--color--ast-global-color-7)!important}.has-ast-global-color-8-border-color{border-color:var(--wp--preset--color--ast-global-color-8)!important}.has-vivid-cyan-blue-to-vivid-purple-gradient-background{background:var(--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple)!important}.has-light-green-cyan-to-vivid-green-cyan-gradient-background{background:var(--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan)!important}.has-luminous-vivid-amber-to-luminous-vivid-orange-gradient-background{background:var(--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange)!important}.has-luminous-vivid-orange-to-vivid-red-gradient-background{background:var(--wp--preset--gradient--luminous-vivid-orange-to-vivid-red)!important}.has-very-light-gray-to-cyan-bluish-gray-gradient-background{background:var(--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray)!important}.has-cool-to-warm-spectrum-gradient-background{background:var(--wp--preset--gradient--cool-to-warm-spectrum)!important}.has-blush-light-purple-gradient-background{background:var(--wp--preset--gradient--blush-light-purple)!important}.has-blush-bordeaux-gradient-background{background:var(--wp--preset--gradient--blush-bordeaux)!important}.has-luminous-dusk-gradient-background{background:var(--wp--preset--gradient--luminous-dusk)!important}.has-pale-ocean-gradient-background{background:var(--wp--preset--gradient--pale-ocean)!important}.has-electric-grass-gradient-background{background:var(--wp--preset--gradient--electric-grass)!important}.has-midnight-gradient-background{background:var(--wp--preset--gradient--midnight)!important}.has-small-font-size{font-size:var(--wp--preset--font-size--small)!important}.has-medium-font-size{font-size:var(--wp--preset--font-size--medium)!important}.has-large-font-size{font-size:var(--wp--preset--font-size--large)!important}.has-x-large-font-size{font-size:var(--wp--preset--font-size--x-large)!important}:root :where(.wp-block-pullquote){font-size:1.5em;line-height:1.6}</style><link rel=stylesheet id=sbttb-fonts-css href="https://123mathe.de/wp-content/plugins/smooth-back-to-top-button/assets/css/sbttb-fonts.css?ezmin=true&ff=1&ver=1.1.14&wps=false" media=all><link rel=stylesheet id=sbttb-style-css href="https://123mathe.de/wp-content/plugins/smooth-back-to-top-button/assets/css/smooth-back-to-top-button.css?ezmin=true&ff=1&ver=1.1.14&wps=false" media=all><script src="https://123mathe.de/wp-includes/js/jquery/jquery.min.js?screx=1&sxcb=10a&ver=3.7.1" id=jquery-core-js type=text/ez-screx></script><script src="https://123mathe.de/wp-includes/js/jquery/jquery-migrate.min.js?screx=1&sxcb=10a&ver=3.4.1" id=jquery-migrate-js type=text/ez-screx></script><link rel=https://api.w.org/ href=https://123mathe.de/wp-json/><link rel=alternate title=JSON type=application/json href=https://123mathe.de/wp-json/wp/v2/posts/1943><link rel=edituri type=application/rsd+xml title=RSD href=https://123mathe.de/xmlrpc.php?rsd><meta name=generator content="WordPress 6.7.2"><link rel=shortlink href="https://123mathe.de/?p=1943"><link rel=alternate title="oEmbed (JSON)" type=application/json+oembed href="https://123mathe.de/wp-json/oembed/1.0/embed?url=https%3A%2F%2F123mathe.de%2Fmengenbegriff"><link rel=alternate title="oEmbed (XML)" type=text/xml+oembed href="https://123mathe.de/wp-json/oembed/1.0/embed?url=https%3A%2F%2F123mathe.de%2Fmengenbegriff&format=xml"><style>.progress-wrap{bottom:50px;height:46px;width:46px;border-radius:46px;background-color:#fff;box-shadow:inset 0 0 0 3px #e2ffe2}.progress-wrap.btn-left-side{left:50px}.progress-wrap.btn-right-side{right:50px}.progress-wrap::after{width:46px;height:46px;color:#d9305d;font-size:24px;content:'\e900';line-height:46px}.progress-wrap:hover::after{color:#1f2029}.progress-wrap svg.progress-circle path{stroke:#d9305d;stroke-width:4px}</style><link rel=icon href=https://123mathe.de/wp-content/uploads/2022/12/cropped-123mahte-logo-klein-32x32.webp sizes=32x32><link rel=icon href=https://123mathe.de/wp-content/uploads/2022/12/cropped-123mahte-logo-klein-192x192.webp sizes=192x192><link rel=apple-touch-icon href=https://123mathe.de/wp-content/uploads/2022/12/cropped-123mahte-logo-klein-180x180.webp><meta name=msapplication-TileImage content="https://123mathe.de/wp-content/uploads/2022/12/cropped-123mahte-logo-klein-270x270.webp"><style id=wp-custom-css>.ast-archive-title,header.entry-header:nth-child(1){padding-bottom:25px;padding-top:25px;border:1px solid #e2ffe2;background-color:#fff}h1{text-align:center}.entry-meta{text-align:center}.archive .entry-meta,.ast-related-post .entry-meta,.ast-grid-common-col .entry-meta{text-align:left!important}pre{background-color:#f6fef6}#astra-footer-menu{display:flex;flex-direction:column;text-transform:uppercase}#menu-item-18443>a:nth-child(1){padding-left:0}#menu-item-18444>a:nth-child(1){padding-left:0}#menu-item-18445>a:nth-child(1){padding-left:0}#menu-item-18446>a:nth-child(1){padding-left:0}#block-27{margin-bottom:10px}.wp-block-latest-posts__list>li:nth-child(1){margin-top:0;margin-bottom:0}.wp-block-latest-posts__list>li:nth-child(2){margin-top:0;margin-bottom:0}.wp-block-latest-posts__list>li:nth-child(3){margin-top:0;margin-bottom:0}.wp-block-latest-posts__list>li:nth-child(4){margin-top:0}.wp-block-latest-posts__list>li:nth-child(1)>a:nth-child(2)>span:nth-child(2){display:none}#colophon{margin-top:100px}@media only screen and (max-width:1000px){.site-footer-above-section-1>aside:nth-child(1){margin-left:10px}.wp-block-latest-posts__list>li:nth-child(2){margin-right:0}.wp-block-latest-posts__list>li:nth-child(1){margin-right:0}.site-above-footer-inner-wrap{display:flex;flex-direction:column;justify-content:center}.site-footer-above-section-2{width:100%;display:flex}.site-footer-above-section-1{width:100%}#astra-footer-menu{flex-direction:row;flex-wrap:wrap;justify-content:center;gap:25px;padding-top:25px}}.ast-single-related-posts-container{background-color:#fff;background-color:#f6fef6}header{background-color:#fff;background-color:#f6fef6}.wp-block-search__label{display:none}@media only screen and (max-width:800px){.site-footer-below-section-1>div:nth-child(1)>div:nth-child(1){margin-left:0;margin-right:10px}.wp-block-latest-posts__list>li:nth-child(3){margin-right:0}.site-footer-below-section-1>div:nth-child(1)>div:nth-child(1)>p:nth-child(2){margin-right:10px}#content>div:nth-child(1){padding-left:5px;padding-right:5px}}.katex-html{font-size:17px}.ast-related-posts-inner-section img,.post-thumb-img-content,.post-navigation{display:none}@media only screen and (min-width:1200px){.wd-table{width:70%;margin:auto;margin-bottom:100px}}.wd-table{margin-bottom:100px}@media only screen and (max-width:600px){.wd-table{width:95%;margin:auto;font-size:14px}table code{font-size:12px}}p{font-size:18px!important}section{padding-top:0;padding-bottom:0}.hdq_question_after_text{background:0 0!important}.btr-zweispaltig{display:flex;flex-direction:row;justify-content:space-evenly;align-items:stretch;border:1px solid #e2ffe2;background-color:#fff;padding-top:25px;padding-bottom:25px;align-items:center}.btr-code{max-width:45%}.btr-beispiel{max-width:45%}code{font-weight:700;font-size:16px}.browaus{border:1px solid #e2ffe2;padding:15px;background-color:#fff;font-family:Arial;margin-bottom:25px}.wp-image-21492{border:1px solid grey;margin-top:25px}.dark{background-color:grey;color:#fff;padding:5px;font-weight:200}.etwas-abstand{margin-bottom:15px}.wp-block-latest-posts__list>li:nth-child(3)>a:nth-child(2)>span:nth-child(2){display:none!important}</style><script>var ezoTemplate='orig_site';var ezouid='1';var ezoFormfactor='1';</script><script data-ezscrex=false>var soc_app_id='0';var did=140745;var ezdomain='123mathe.de';var ezoicSearchable=1;</script><script data-cfasync=false>__ez.queue.addFile('/tardisrocinante/lazy_load.js','/tardisrocinante/lazy_load.js?gcb=4&cb=6',false,[],true,false,true,false);</script><link rel=preload as=font href=https://123mathe.de/wp-content/plugins/smooth-back-to-top-button/assets/fonts/wpxpress.woff?9zg56 crossorigin></head><body itemtype=https://schema.org/Blog itemscope class="post-template-default single single-post postid-1943 single-format-standard ast-desktop ast-plain-container ast-no-sidebar astra-4.8.12 group-blog ast-blog-single-style-1 ast-single-post ast-inherit-site-logo-transparent ast-hfb-header ast-normal-title-enabled"><a class="skip-link screen-reader-text" href=#content title="Zum Inhalt springen">Zum Inhalt springen</a><div class="hfeed site" id=page><header class="site-header header-main-layout-1 ast-primary-menu-enabled ast-logo-title-inline ast-hide-custom-menu-mobile ast-builder-menu-toggle-icon ast-mobile-header-inline" id=masthead itemtype=https://schema.org/WPHeader itemscope itemid=#masthead><div id=ast-desktop-header data-toggle-type=dropdown><div class="ast-main-header-wrap main-header-bar-wrap"><div class="ast-primary-header-bar ast-primary-header main-header-bar site-header-focus-item" data-section=section-primary-header-builder><div class="site-primary-header-wrap ast-builder-grid-row-container site-header-focus-item ast-container" data-section=section-primary-header-builder><div class="ast-builder-grid-row ast-builder-grid-row-has-sides ast-builder-grid-row-no-center"><div class="site-header-primary-section-left site-header-section ast-flex site-header-section-left"><div class="ast-builder-layout-element ast-flex site-header-focus-item" data-section=title_tagline><div class="site-branding ast-site-identity" itemtype=https://schema.org/Organization itemscope><div class=ast-site-title-wrap><span class=site-title itemprop=name><a href=https://123mathe.de/ rel=home itemprop=url>123mathe</a></span><p class=site-description itemprop=description>Mathematik und Physik für Schüler, Lehrer und Eltern</div></div></div></div><div class="site-header-primary-section-right site-header-section ast-flex ast-grid-right-section"><div class="ast-builder-menu-1 ast-builder-menu ast-flex ast-builder-menu-1-focus-item ast-builder-layout-element site-header-focus-item" data-section=section-hb-menu-1><div class=ast-main-header-bar-alignment><div class=main-header-bar-navigation><nav class="site-navigation ast-flex-grow-1 navigation-accessibility site-header-focus-item" id=primary-site-navigation-desktop aria-label="Website-Navigation: Navigation" itemtype=https://schema.org/SiteNavigationElement itemscope><div class="main-navigation ast-inline-flex"><ul id=ast-hf-menu-1 class="main-header-menu ast-menu-shadow ast-nav-menu ast-flex submenu-with-border stack-on-mobile"><li id=menu-item-6446 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-has-children menu-item-6446"><a aria-expanded=false href=https://123mathe.de/mathe-gesamtuebersicht class=menu-link>Mathematik<span role=application class="dropdown-menu-toggle ast-header-navigation-arrow" tabindex=0 aria-expanded=false aria-label="Menü umschalten"><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span></span></a><button class=ast-menu-toggle aria-expanded=false><span class=screen-reader-text>Menü umschalten</span><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span></button><ul class=sub-menu><li id=menu-item-10989 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-10989"><a href=https://123mathe.de/mathe-gesamtuebersicht class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Mathematik Gesamtübersicht</a><li id=menu-item-8765 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8765"><a href=https://123mathe.de/mathematik-aufgabensammlung-uebersicht class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Mathematik Aufgabensammlung</a><li id=menu-item-8819 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8819"><a href=https://123mathe.de/wiederholung-sekundarstufe-i-uebersicht class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Sekundarstufe 1</a><li id=menu-item-11823 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-11823"><a href=https://123mathe.de/mathematik-sekundarstufe-2 class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Sekundarstufe 2</a><li id=menu-item-8752 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8752"><a href=https://123mathe.de/unterrichtsthemen-und-aufgaben-zur-abiturvorbereitung class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Themen und Aufgaben zur Abiturvorbereitung</a><li id=menu-item-8750 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8750"><a href=https://123mathe.de/interaktive-mathematische-programme class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Interaktive mathematische Programme</a><li id=menu-item-8826 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8826"><a href=https://123mathe.de/mathematik-im-berufsgrundschuljahr-uebersicht class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Berufsgrundschuljahr</a></ul><li id=menu-item-6448 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-has-children menu-item-6448"><a aria-expanded=false href=https://123mathe.de/physik-gesamtuebersicht class=menu-link>Physik<span role=application class="dropdown-menu-toggle ast-header-navigation-arrow" tabindex=0 aria-expanded=false aria-label="Menü umschalten"><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span></span></a><button class=ast-menu-toggle aria-expanded=false><span class=screen-reader-text>Menü umschalten</span><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span></button><ul class=sub-menu><li id=menu-item-11201 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-11201"><a href=https://123mathe.de/physik-gesamtuebersicht class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Physik Gesamtübersicht</a><li id=menu-item-8779 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8779"><a href=https://123mathe.de/physik-aufgabensammlung-uebersicht class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Physik Aufgabensammlung</a><li id=menu-item-8778 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8778"><a href=https://123mathe.de/physik-uebersicht-elektrizitaet-und-waerme class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Elektrizität und Wärme</a><li id=menu-item-8777 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8777"><a href=https://123mathe.de/uebersicht-physik-schall-laerm-licht-und-sehen class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Schall, Lärm, Licht und Sehen</a><li id=menu-item-8776 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8776"><a href=https://123mathe.de/uebersicht-physik-mechanik-festkoerper-und-fluessigkeiten class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Mechanik, Festkörper, Flüssigkeiten</a><li id=menu-item-8775 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8775"><a href=https://123mathe.de/uebersicht-physik-messungen-im-stromkreis-elektromagnete-klasse-8 class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Stromkreis messen, Elektromagnete</a><li id=menu-item-8774 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8774"><a href=https://123mathe.de/physik-uebersicht-strahlenoptik class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Strahlenoptik, Induktion</a><li id=menu-item-8773 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8773"><a href=https://123mathe.de/physik-uebersicht-physik-mechanik-und-elektronik-klasse-10 class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Mechanik</a><li id=menu-item-8772 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8772"><a href=https://123mathe.de/physik-uebersicht-elektronik-klasse-10 class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Elektronik</a><li id=menu-item-8771 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8771"><a href=https://123mathe.de/physik-uebersicht-oberstufenphysik class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Oberstufenphysik</a></ul><li id=menu-item-6482 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-6482"><a href=https://123mathe.de/technik-uebersicht class=menu-link>Technik</a><li id=menu-item-11934 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-11934"><a href=https://123mathe.de/geraetekunde-uebersicht class=menu-link>Gerätekunde</a><li id=menu-item-22243 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-22243"><a href=https://123mathe.de/videos-123mathe class=menu-link>Videos</a><li id=menu-item-22247 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-22247"><a href=https://123mathe.de/pdf-und-word-dateien class=menu-link>PDF/WORD</a></ul></div></nav></div></div></div><div class="ast-builder-layout-element ast-flex site-header-focus-item ast-header-search" data-section=section-header-search><div class="ast-search-menu-icon slide-search"><form role=search class=search-form action=https://123mathe.de/><label for=search-field><span class=screen-reader-text>Suchen nach:</span> <input type=search id=search-field class=search-field placeholder=Suchen … name=s tabindex=-1> <button class="search-submit ast-search-submit" aria-label="Suche übermitteln"> <span hidden>Suchen</span> <i><span class="ast-icon icon-search"><svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" viewBox="-893 477 142 142" enable-background="new -888 480 142 142" xml:space="preserve"> <path d="M-787.4,568.7h-6.3l-2.4-2.4c7.9-8.7,12.6-20.5,12.6-33.1c0-28.4-22.9-51.3-51.3-51.3 c-28.4,0-51.3,22.9-51.3,51.3c0,28.4,22.9,51.3,51.3,51.3c12.6,0,24.4-4.7,33.1-12.6l2.4,2.4v6.3l39.4,39.4l11.8-11.8L-787.4,568.7 L-787.4,568.7z M-834.7,568.7c-19.7,0-35.5-15.8-35.5-35.5c0-19.7,15.8-35.5,35.5-35.5c19.7,0,35.5,15.8,35.5,35.5 C-799.3,553-815,568.7-834.7,568.7L-834.7,568.7z"></path> </svg></span></i></button></label></form><div class=ast-search-icon><a class="slide-search astra-search-icon" aria-label="Link des Such-Icons" href=#><span class=screen-reader-text>Suchen</span> <span class="ast-icon icon-search"><svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" viewBox="-893 477 142 142" enable-background="new -888 480 142 142" xml:space="preserve"> <path d="M-787.4,568.7h-6.3l-2.4-2.4c7.9-8.7,12.6-20.5,12.6-33.1c0-28.4-22.9-51.3-51.3-51.3 c-28.4,0-51.3,22.9-51.3,51.3c0,28.4,22.9,51.3,51.3,51.3c12.6,0,24.4-4.7,33.1-12.6l2.4,2.4v6.3l39.4,39.4l11.8-11.8L-787.4,568.7 L-787.4,568.7z M-834.7,568.7c-19.7,0-35.5-15.8-35.5-35.5c0-19.7,15.8-35.5,35.5-35.5c19.7,0,35.5,15.8,35.5,35.5 C-799.3,553-815,568.7-834.7,568.7L-834.7,568.7z"></path> </svg></span></a></div></div></div></div></div></div></div></div></div><div id=ast-mobile-header class=ast-mobile-header-wrap data-type=dropdown><div class="ast-main-header-wrap main-header-bar-wrap"><div class="ast-primary-header-bar ast-primary-header main-header-bar site-primary-header-wrap site-header-focus-item ast-builder-grid-row-layout-default ast-builder-grid-row-tablet-layout-default ast-builder-grid-row-mobile-layout-default" data-section=section-primary-header-builder><div class="ast-builder-grid-row ast-builder-grid-row-has-sides ast-builder-grid-row-no-center"><div class="site-header-primary-section-left site-header-section ast-flex site-header-section-left"><div class="ast-builder-layout-element ast-flex site-header-focus-item" data-section=title_tagline><div class="site-branding ast-site-identity" itemtype=https://schema.org/Organization itemscope><div class=ast-site-title-wrap><span class=site-title itemprop=name><a href=https://123mathe.de/ rel=home itemprop=url>123mathe</a></span><p class=site-description itemprop=description>Mathematik und Physik für Schüler, Lehrer und Eltern</div></div></div></div><div class="site-header-primary-section-right site-header-section ast-flex ast-grid-right-section"><div class="ast-builder-layout-element ast-flex site-header-focus-item" data-section=section-header-mobile-trigger><div class=ast-button-wrap><button type=button class="menu-toggle main-header-menu-toggle ast-mobile-menu-trigger-outline" aria-expanded=false> <span class=screen-reader-text>Main Menu</span> <span class=mobile-menu-toggle-icon><span aria-hidden=true class="ahfb-svg-iconset ast-inline-flex svg-baseline"><svg class="ast-mobile-svg ast-menu2-svg" fill="currentColor" version="1.1" xmlns="http://www.w3.org/2000/svg" width="24" height="28" viewBox="0 0 24 28"><path d="M24 21v2c0 0.547-0.453 1-1 1h-22c-0.547 0-1-0.453-1-1v-2c0-0.547 0.453-1 1-1h22c0.547 0 1 0.453 1 1zM24 13v2c0 0.547-0.453 1-1 1h-22c-0.547 0-1-0.453-1-1v-2c0-0.547 0.453-1 1-1h22c0.547 0 1 0.453 1 1zM24 5v2c0 0.547-0.453 1-1 1h-22c-0.547 0-1-0.453-1-1v-2c0-0.547 0.453-1 1-1h22c0.547 0 1 0.453 1 1z"></path></svg></span><span aria-hidden=true class="ahfb-svg-iconset ast-inline-flex svg-baseline"><svg class="ast-mobile-svg ast-close-svg" fill="currentColor" version="1.1" xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24"><path d="M5.293 6.707l5.293 5.293-5.293 5.293c-0.391 0.391-0.391 1.024 0 1.414s1.024 0.391 1.414 0l5.293-5.293 5.293 5.293c0.391 0.391 1.024 0.391 1.414 0s0.391-1.024 0-1.414l-5.293-5.293 5.293-5.293c0.391-0.391 0.391-1.024 0-1.414s-1.024-0.391-1.414 0l-5.293 5.293-5.293-5.293c-0.391-0.391-1.024-0.391-1.414 0s-0.391 1.024 0 1.414z"></path></svg></span></span></button></div></div><div class="ast-builder-layout-element ast-flex site-header-focus-item ast-header-search" data-section=section-header-search><div class="ast-search-menu-icon slide-search"><form role=search class=search-form action=https://123mathe.de/><label for=search-field><span class=screen-reader-text>Suchen nach:</span> <input type=search id=search-field class=search-field placeholder=Suchen … name=s tabindex=-1> <button class="search-submit ast-search-submit" aria-label="Suche übermitteln"> <span hidden>Suchen</span> <i><span class="ast-icon icon-search"><svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" viewBox="-893 477 142 142" enable-background="new -888 480 142 142" xml:space="preserve"> <path d="M-787.4,568.7h-6.3l-2.4-2.4c7.9-8.7,12.6-20.5,12.6-33.1c0-28.4-22.9-51.3-51.3-51.3 c-28.4,0-51.3,22.9-51.3,51.3c0,28.4,22.9,51.3,51.3,51.3c12.6,0,24.4-4.7,33.1-12.6l2.4,2.4v6.3l39.4,39.4l11.8-11.8L-787.4,568.7 L-787.4,568.7z M-834.7,568.7c-19.7,0-35.5-15.8-35.5-35.5c0-19.7,15.8-35.5,35.5-35.5c19.7,0,35.5,15.8,35.5,35.5 C-799.3,553-815,568.7-834.7,568.7L-834.7,568.7z"></path> </svg></span></i></button></label></form><div class=ast-search-icon><a class="slide-search astra-search-icon" aria-label="Link des Such-Icons" href=#><span class=screen-reader-text>Suchen</span> <span class="ast-icon icon-search"><svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" viewBox="-893 477 142 142" enable-background="new -888 480 142 142" xml:space="preserve"> <path d="M-787.4,568.7h-6.3l-2.4-2.4c7.9-8.7,12.6-20.5,12.6-33.1c0-28.4-22.9-51.3-51.3-51.3 c-28.4,0-51.3,22.9-51.3,51.3c0,28.4,22.9,51.3,51.3,51.3c12.6,0,24.4-4.7,33.1-12.6l2.4,2.4v6.3l39.4,39.4l11.8-11.8L-787.4,568.7 L-787.4,568.7z M-834.7,568.7c-19.7,0-35.5-15.8-35.5-35.5c0-19.7,15.8-35.5,35.5-35.5c19.7,0,35.5,15.8,35.5,35.5 C-799.3,553-815,568.7-834.7,568.7L-834.7,568.7z"></path> </svg></span></a></div></div></div></div></div></div></div><div class="ast-mobile-header-content content-align-flex-start"><div class="ast-builder-menu-mobile ast-builder-menu ast-builder-menu-mobile-focus-item ast-builder-layout-element site-header-focus-item" data-section=section-header-mobile-menu><div class=ast-main-header-bar-alignment><div class=main-header-bar-navigation><nav class="site-navigation ast-flex-grow-1 navigation-accessibility site-header-focus-item" id=ast-mobile-site-navigation aria-label="Website-Navigation: Navigation" itemtype=https://schema.org/SiteNavigationElement itemscope><div class=main-navigation><ul id=ast-hf-mobile-menu class="main-header-menu ast-nav-menu ast-flex submenu-with-border astra-menu-animation-fade stack-on-mobile"><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-has-children menu-item-6446"><a aria-expanded=false href=https://123mathe.de/mathe-gesamtuebersicht class=menu-link>Mathematik<span role=application class="dropdown-menu-toggle ast-header-navigation-arrow" tabindex=0 aria-expanded=false aria-label="Menü umschalten"><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span></span></a><button class=ast-menu-toggle aria-expanded=false><span class=screen-reader-text>Menü umschalten</span><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span></button><ul class=sub-menu><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-10989"><a href=https://123mathe.de/mathe-gesamtuebersicht class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Mathematik Gesamtübersicht</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8765"><a href=https://123mathe.de/mathematik-aufgabensammlung-uebersicht class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Mathematik Aufgabensammlung</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8819"><a href=https://123mathe.de/wiederholung-sekundarstufe-i-uebersicht class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Sekundarstufe 1</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-11823"><a href=https://123mathe.de/mathematik-sekundarstufe-2 class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Sekundarstufe 2</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8752"><a href=https://123mathe.de/unterrichtsthemen-und-aufgaben-zur-abiturvorbereitung class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Themen und Aufgaben zur Abiturvorbereitung</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8750"><a href=https://123mathe.de/interaktive-mathematische-programme class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Interaktive mathematische Programme</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8826"><a href=https://123mathe.de/mathematik-im-berufsgrundschuljahr-uebersicht class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Berufsgrundschuljahr</a></ul><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-has-children menu-item-6448"><a aria-expanded=false href=https://123mathe.de/physik-gesamtuebersicht class=menu-link>Physik<span role=application class="dropdown-menu-toggle ast-header-navigation-arrow" tabindex=0 aria-expanded=false aria-label="Menü umschalten"><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span></span></a><button class=ast-menu-toggle aria-expanded=false><span class=screen-reader-text>Menü umschalten</span><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span></button><ul class=sub-menu><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-11201"><a href=https://123mathe.de/physik-gesamtuebersicht class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Physik Gesamtübersicht</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8779"><a href=https://123mathe.de/physik-aufgabensammlung-uebersicht class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Physik Aufgabensammlung</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8778"><a href=https://123mathe.de/physik-uebersicht-elektrizitaet-und-waerme class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Elektrizität und Wärme</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8777"><a href=https://123mathe.de/uebersicht-physik-schall-laerm-licht-und-sehen class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Schall, Lärm, Licht und Sehen</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8776"><a href=https://123mathe.de/uebersicht-physik-mechanik-festkoerper-und-fluessigkeiten class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Mechanik, Festkörper, Flüssigkeiten</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8775"><a href=https://123mathe.de/uebersicht-physik-messungen-im-stromkreis-elektromagnete-klasse-8 class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Stromkreis messen, Elektromagnete</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8774"><a href=https://123mathe.de/physik-uebersicht-strahlenoptik class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Strahlenoptik, Induktion</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8773"><a href=https://123mathe.de/physik-uebersicht-physik-mechanik-und-elektronik-klasse-10 class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Mechanik</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8772"><a href=https://123mathe.de/physik-uebersicht-elektronik-klasse-10 class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Elektronik</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-8771"><a href=https://123mathe.de/physik-uebersicht-oberstufenphysik class=menu-link><span class="ast-icon icon-arrow"><svg class="ast-arrow-svg" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" x="0px" y="0px" width="26px" height="16.043px" viewBox="57 35.171 26 16.043" enable-background="new 57 35.171 26 16.043" xml:space="preserve"> <path d="M57.5,38.193l12.5,12.5l12.5-12.5l-2.5-2.5l-10,10l-10-10L57.5,38.193z"></path> </svg></span>Oberstufenphysik</a></ul><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-6482"><a href=https://123mathe.de/technik-uebersicht class=menu-link>Technik</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-11934"><a href=https://123mathe.de/geraetekunde-uebersicht class=menu-link>Gerätekunde</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-22243"><a href=https://123mathe.de/videos-123mathe class=menu-link>Videos</a><li class="menu-item menu-item-type-post_type menu-item-object-post menu-item-22247"><a href=https://123mathe.de/pdf-und-word-dateien class=menu-link>PDF/WORD</a></ul></div></nav></div></div></div></div></div></header><div id=content class=site-content><div class=ast-container><div id=primary class="content-area primary"><main id=main class=site-main><article class="post-1943 post type-post status-publish format-standard hentry category-aussagen-und-mengen category-mathematik ast-article-single" id=post-1943 itemtype=https://schema.org/CreativeWork itemscope><div class="ast-post-format- ast-no-thumb single-layout-1"><header class="entry-header ast-no-thumbnail"><h1 class=entry-title itemprop=headline>Mengenbegriff in der Mengenlehre</h1><div class=entry-meta><span class=ast-terms-link><a href=https://123mathe.de/category/mathematik/aussagen-und-mengen>Aussagen und Mengen</a>, <a href=https://123mathe.de/category/mathematik>Mathematik</a></span></div></header><div class="entry-content clear" itemprop=text><p>In diesem Beitrag gebe ich eine Einführung in die Mengenlehre. Zuerst <strong>definiere</strong> ich die wichtigen<strong> Begriffe: Mathematische Definition der Menge, Elemente, Objekte, leere Menge</strong>. Danach stelle ich die <strong>Darstellung von Mengen, die Mengenschreibweise in beschreibender Form</strong> und die <strong>Darstellung einer Menge im Mengendiagramm </strong>vor. Anschließend verdeutliche ich dies anhand von <strong>Beispielen</strong>.<h2><b class=def>Mathematische Definition der </b><b class=def>Menge</b><b class=def>:</b></h2><p>Eine <strong><i class=merk>Menge</i></strong> ist die Zusammenfassung bestimmter, wohlunterschiedener <strong><i class=merk>Objekte </i></strong>zu einem Ganzen. Diese Objekte werden <strong><i class=merk>Elemente</i> </strong>der Menge genannt werden<strong><i>.</i></strong><br>Bitte verwechselt Sie jedoch den Mengenbegriff nicht mit dem umgangssprachlichen Begriff Menge im Sinne von viel!<br>In der Definition bedeutet <strong>bestimmte Objekte</strong>, dass man genau entscheiden muss, ob das Element zur Menge gehört.<br>Wohlunterschieden bedeutet, dass jedes Element nur einmal in der Menge enthalten ist. Es dürfen also nicht mehrere gleiche Elemente in einer Menge vorhanden sein. Das mehrfach vorkommende Element wird dabei nur einmal in der Menge aufgeführt. Eine Menge, die kein Element enthält, wird <strong><i class=merk>leere Menge</i></strong> genannt.<br>Im folgenden stelle ich Beispiele aus der Mathematik vor.<p>Mengen werden dargestellt mit Hilfe der <strong><i class=merk>Mengenklammern,</i> </strong>in denen man die Elemente aufzählt.<p>Eine andere Darstellung ist das Mengendiagramm (<strong><i class=merk>Euler</i> </strong>– oder <strong><i class=merk>Venn</i> </strong>– Diagramm). Dabei werden die Elemente in das Diagramm eingetragen.<hr noshade size=1><p> <h2 class=px>Darstellung von Mengen</h2><div class=px><p>Symbole für Mengen sind große Buchstaben, z.B. A, B, M, …..<br>Symbole für Elemente sind z.B. kleine Buchstaben oder auch Zahlen a, b, c, x, y, …1, 2, 3, 99, …..<br>Mengenschreibweise in <strong>aufzählender Form</strong>: A = {a; b; c; d}<p>Dies spricht man so aus: A ist die Menge mit den Elementen a, b, c, d<p><img decoding=async src=https://www.brinkmann-du.de/mathe/fos/formel/f_560.gif alt=f_560 width=300 height=45 border=0><p><img decoding=async src=https://www.brinkmann-du.de/mathe/fos/formel/f_561.gif alt=f_561 width=564 height=77 border=0><p><img decoding=async src=https://www.brinkmann-du.de/mathe/fos/formel/f_562.gif alt=f_562 width=384 height=26 border=0><h2>Mengenschreibweise in beschreibender Form:</h2><p><img loading=lazy decoding=async src=https://www.brinkmann-du.de/mathe/fos/formel/f_563.gif alt=f_563 width=360 height=21 border=0><p>Dies spricht man so aus: B ist die Menge aller Elemente x, für die gilt: x ist größer oder gleich -3 und kleiner oder gleich 1 und x ist eine ganze Zahl.</div><h2>Darstellung einer Menge im Mengendiagramm:</h2><p><img loading=lazy decoding=async src=https://www.brinkmann-du.de/mathe/fos/designer/des_050.gif alt=des_050 width=186 height=157 border=0><h3><b class=sfbeispiel>Beispiel:</b></h3><p>Geben Sie die Menge der geraden natürlichen Zahlen zwischen 9 und 25 an! Und zwar in aufzählender und beschreibender Form sowie im Mengendiagramm.<p><img loading=lazy decoding=async src=https://www.brinkmann-du.de/mathe/fos/formel/f_564.gif alt=f_564 width=373 height=26 border=0><p><img loading=lazy decoding=async src=https://www.brinkmann-du.de/mathe/fos/formel/f_565.gif alt=f_565 width=612 height=21 border=0><p>Mengendiagramm: <img loading=lazy decoding=async src=https://www.brinkmann-du.de/mathe/fos/designer/des_051.gif alt=des_051 width=205 height=138 align=middle border=0><h3><b class=sfbeispiel>Beispiel:</b></h3><p>Die Menge A ist in aufzählender Form geschrieben. Enwickeln Sie eine beschreibende Form!<p><img loading=lazy decoding=async src=https://www.brinkmann-du.de/mathe/fos/formel/f_566.gif alt=f_566 width=481 height=76 border=0><p>Im nächsten Beitrag geht es um <a href=https://123mathe.de/mengen-eigenschaften>Eigenschaften von Mengen.</a><p><strong>Hier findest du eine <a href=https://123mathe.de/aussagen-und-mengen-uebersicht>Übersicht über alle Beiträge und Aufgaben zum Thema Aussagen und Mengen</a>, darin auch Links zu Aufgaben.</strong></div></div></article><nav class="navigation post-navigation" aria-label=Beitragsnavigation><span class=screen-reader-text>Beitragsnavigation</span><div class=nav-links><div class=nav-previous><a title="Verknüpfung von Aussagen in der Mathematik" href=https://123mathe.de/verknuepfung-von-aussagen rel=prev><span class=ast-left-arrow>←</span> Vorheriger Beitrag</a></div><div class=nav-next><a title="Eigenschaften von Mengen" href=https://123mathe.de/mengen-eigenschaften rel=next>Nächster Beitrag <span class=ast-right-arrow>→</span></a></div></div></nav><div class="ast-single-related-posts-container ast-container--fallback"><div class=ast-related-posts-title-section><h2 class=ast-related-posts-title>Ähnliche Beiträge</h2></div><div class=ast-related-posts-wrapper><article class="ast-related-post post-72 post type-post status-publish format-standard has-post-thumbnail hentry category-bruchrechnen category-mathematik category-sekundarstufe-1"><div class=ast-related-posts-inner-section><div class=ast-related-post-content><div class="ast-related-post-featured-section post-has-thumb"><div class="post-thumb-img-content post-thumb"><a aria-label="Mehr Informationen über Dezimalbrüche einfach erklärt" href=https://123mathe.de/dezimalbrueche><img width=500 height=667 src="data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20width=%22500%22%20height=%22667%22%3E%3C/svg%3E" class="ezlazyload attachment-large size-large wp-post-image" alt="Darstellung vier Sechstel einer Pizza" itemprop decoding=async loading=lazy data-ezsrcset="https://123mathe.de/wp-content/uploads/2018/01/Bruch-4-6-Kopie.jpg 500w,https://123mathe.de/wp-content/uploads/2018/01/Bruch-4-6-Kopie-225x300.jpg 225w" sizes="auto, (max-width: 500px) 100vw, 500px" ezimgfmt="rs rscb10 src ng ngcb10 srcset" data-ezsrc=https://123mathe.de/wp-content/uploads/2018/01/Bruch-4-6-Kopie.jpg></a></div></div><header class="entry-header related-entry-header"><h3 class="ast-related-post-title entry-title"><a href=https://123mathe.de/dezimalbrueche target=_self rel="bookmark noopener noreferrer">Dezimalbrüche einfach erklärt</a></h3><div class="entry-meta ast-related-cat-style--none ast-related-tag-style--none"><span class="ast-taxonomy-container cat-links default"><a href=https://123mathe.de/category/mathematik/sekundarstufe-1/bruchrechnen rel="category tag">Bruchrechnen</a>, <a href=https://123mathe.de/category/mathematik rel="category tag">Mathematik</a>, <a href=https://123mathe.de/category/mathematik/sekundarstufe-1 rel="category tag">Sekundarstufe 1</a></span></div></header><div class="entry-content clear"></div></div></div></article><article class="ast-related-post post-88 post type-post status-publish format-standard hentry category-bruchrechnen category-mathematik category-sekundarstufe-1 tag-brueche-dividieren tag-brueche-multiplizieren tag-brueche-subtrahieren tag-bruchzahlen"><div class=ast-related-posts-inner-section><div class=ast-related-post-content><div class="ast-related-post-featured-section ast-no-thumb"></div><header class="entry-header related-entry-header"><h3 class="ast-related-post-title entry-title"><a href=https://123mathe.de/brueche target=_self rel="bookmark noopener noreferrer">Bruchrechnen einfach erklärt</a></h3><div class="entry-meta ast-related-cat-style--none ast-related-tag-style--none"><span class="ast-taxonomy-container cat-links default"><a href=https://123mathe.de/category/mathematik/sekundarstufe-1/bruchrechnen rel="category tag">Bruchrechnen</a>, <a href=https://123mathe.de/category/mathematik rel="category tag">Mathematik</a>, <a href=https://123mathe.de/category/mathematik/sekundarstufe-1 rel="category tag">Sekundarstufe 1</a></span></div></header><div class="entry-content clear"></div></div></div></article><article class="ast-related-post post-106 post type-post status-publish format-standard hentry category-aufgabensammlung category-bruchrechnen category-mathematik category-sekundarstufe-1 tag-brueche-addieren tag-dezimalbrueche"><div class=ast-related-posts-inner-section><div class=ast-related-post-content><div class="ast-related-post-featured-section ast-no-thumb"></div><header class="entry-header related-entry-header"><h3 class="ast-related-post-title entry-title"><a href=https://123mathe.de/bruchrechnen-aufgaben1 target=_self rel="bookmark noopener noreferrer">Bruchrechnen Aufgaben I</a></h3><div class="entry-meta ast-related-cat-style--none ast-related-tag-style--none"><span class="ast-taxonomy-container cat-links default"><a href=https://123mathe.de/category/aufgabensammlung rel="category tag">Aufgabensammlung</a>, <a href=https://123mathe.de/category/mathematik/sekundarstufe-1/bruchrechnen rel="category tag">Bruchrechnen</a>, <a href=https://123mathe.de/category/mathematik rel="category tag">Mathematik</a>, <a href=https://123mathe.de/category/mathematik/sekundarstufe-1 rel="category tag">Sekundarstufe 1</a></span></div></header><div class="entry-content clear"></div></div></div></article><article class="ast-related-post post-218 post type-post status-publish format-standard has-post-thumbnail hentry category-aufgabensammlung category-bruchrechnen category-mathematik category-sekundarstufe-1 tag-brueche-addieren tag-brueche-dividieren tag-brueche-multiplizieren tag-brueche-subtrahieren tag-bruchzahlen tag-dezimalbrueche"><div class=ast-related-posts-inner-section><div class=ast-related-post-content><div class="ast-related-post-featured-section post-has-thumb"><div class="post-thumb-img-content post-thumb"><a aria-label="Mehr Informationen über Bruchrechnen Lösungen der Aufgaben mit komplettem Lösungsweg" href=https://123mathe.de/bruchrechnen-regel-loesungen-der-aufgaben><img width=768 height=1024 src="data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20width=%22768%22%20height=%221024%22%3E%3C/svg%3E" class="ezlazyload attachment-large size-large wp-post-image" alt="9 Zwölftel einer Pizza zur Veranschaulichung der Bruchrechnung" itemprop decoding=async loading=lazy data-ezsrcset="https://123mathe.de/wp-content/uploads/2018/01/Bruch-3-4-768x1024.jpg 768w,https://123mathe.de/wp-content/uploads/2018/01/Bruch-3-4-225x300.jpg 225w,https://123mathe.de/wp-content/uploads/2018/01/Bruch-3-4-1152x1536.jpg 1152w,https://123mathe.de/wp-content/uploads/2018/01/Bruch-3-4-1536x2048.jpg 1536w,https://123mathe.de/wp-content/uploads/2018/01/Bruch-3-4-scaled.jpg 1920w" sizes="auto, (max-width: 768px) 100vw, 768px" ezimgfmt="rs rscb10 src ng ngcb10 srcset" data-ezsrc=https://123mathe.de/wp-content/uploads/2018/01/Bruch-3-4-768x1024.jpg></a></div></div><header class="entry-header related-entry-header"><h3 class="ast-related-post-title entry-title"><a href=https://123mathe.de/bruchrechnen-regel-loesungen-der-aufgaben target=_self rel="bookmark noopener noreferrer">Bruchrechnen Lösungen der Aufgaben mit komplettem Lösungsweg</a></h3><div class="entry-meta ast-related-cat-style--none ast-related-tag-style--none"><span class="ast-taxonomy-container cat-links default"><a href=https://123mathe.de/category/aufgabensammlung rel="category tag">Aufgabensammlung</a>, <a href=https://123mathe.de/category/mathematik/sekundarstufe-1/bruchrechnen rel="category tag">Bruchrechnen</a>, <a href=https://123mathe.de/category/mathematik rel="category tag">Mathematik</a>, <a href=https://123mathe.de/category/mathematik/sekundarstufe-1 rel="category tag">Sekundarstufe 1</a></span></div></header><div class="entry-content clear"></div></div></div></article></div></div></main></div></div></div><footer class=site-footer id=colophon itemtype=https://schema.org/WPFooter itemscope itemid=#colophon><div class="site-above-footer-wrap ast-builder-grid-row-container site-footer-focus-item ast-builder-grid-row-2-equal ast-builder-grid-row-tablet-2-equal ast-builder-grid-row-mobile-full ast-footer-row-stack ast-footer-row-tablet-stack ast-footer-row-mobile-stack" data-section=section-above-footer-builder><div class=ast-builder-grid-row-container-inner><div class="ast-builder-footer-grid-columns site-above-footer-inner-wrap ast-builder-grid-row"><div class="site-footer-above-section-1 site-footer-section site-footer-section-1"><aside class="footer-widget-area widget-area site-footer-focus-item footer-widget-area-inner" data-section=sidebar-widgets-footer-widget-1 aria-label="Footer Widget 1"><section id=block-18 class="widget widget_block widget_search"><form role=search action=https://123mathe.de/ class="wp-block-search__button-outside wp-block-search__text-button wp-block-search"><label class=wp-block-search__label for=wp-block-search__input-1>Suchen</label><div class=wp-block-search__inside-wrapper><input class=wp-block-search__input id=wp-block-search__input-1 placeholder type=search name=s required><button aria-label=Suchen class="wp-block-search__button wp-element-button">Suchen</button></div></form></section><section id=block-23 class="widget widget_block widget_categories"><div class="wp-block-categories-dropdown wp-block-categories"><label class=wp-block-categories__label for=wp-block-categories-1>Kategorien</label><select name=category_name id=wp-block-categories-1 class=postform><option value=-1>Kategorie auswählen<option class=level-0 value=aufgabensammlung>Aufgabensammlung (445)<option class=level-1 value=multiple-choice-tests> Multiple Choice Tests (9)<option class=level-0 value=geraetekunde>Gerätekunde (7)<option class=level-0 value=mathematik>Mathematik (590)<option class=level-1 value=abiturvorbereitung> Abiturvorbereitung (21)<option class=level-1 value=aussagen-und-mengen> Aussagen und Mengen (17)<option class=level-1 value=differentialrechnung> Differentialrechnung (87)<option class=level-1 value=funktionen> Funktionen (180)<option class=level-2 value=e-funktion> e-Funktion (37)<option class=level-2 value=exponentialfunktionen> Exponentialfunktionen (22)<option class=level-2 value=ganzrationale-funktionen-mathematik> Ganzrationale Funktionen (96)<option class=level-3 value=lineare-funktionen> Lineare Funktionen (32)<option class=level-3 value=quadratische-funktionen> Quadratische Funktionen (28)<option class=level-3 value=weitere-ganzrationale-funktionen> weitere Ganzrationale Funktionen (13)<option class=level-2 value=logarithmusfunktionen> Logarithmusfunktionen (12)<option class=level-1 value=geometrie> Geometrie (21)<option class=level-1 value=gtr-grafikfaehiger-taschenrechner> GTR grafikfähiger Taschenrechner (27)<option class=level-1 value=integralrechnung> Integralrechnung (63)<option class=level-1 value=sekundarstufe-1> Sekundarstufe 1 (169)<option class=level-2 value=bruchrechnen> Bruchrechnen (20)<option class=level-2 value=dreisatz> Dreisatz (8)<option class=level-2 value=gleichungen> Gleichungen (58)<option class=level-3 value=exponentialgleichungen> Exponentialgleichungen (4)<option class=level-3 value=lineare-gleichungen> Lineare Gleichungen (16)<option class=level-3 value=quadratische-gleichungen> Quadratische Gleichungen (10)<option class=level-2 value=interaktive-trainer> Interaktive Trainer (1)<option class=level-2 value=polynomgleichungen> Polynomgleichungen (7)<option class=level-2 value=potenzen> Potenzen (40)<option class=level-2 value=prozentrechnen> Prozentrechnen (10)<option class=level-2 value=terme> Terme (23)<option class=level-2 value=zinsrechnung> Zinsrechnung (14)<option class=level-1 value=statistik> Statistik (36)<option class=level-1 value=vektorrechnung> Vektorrechnung (10)<option class=level-1 value=wahrscheinlichkeitsrechnung> Wahrscheinlichkeitsrechnung (73)<option class=level-0 value=oberstufe>Oberstufe (6)<option class=level-0 value=physik>Physik (182)<option class=level-1 value=elektrizitaet-und-waerme> Elektrizität, Wärme, Magnetismus Klasse 5 (36)<option class=level-1 value=elektronik-klasse-10> Elektronik Klasse 10 (8)<option class=level-1 value=mechanik-und-elektronik> Mechanik Klasse 10 (21)<option class=level-1 value=mechanik-festkoerper-und-fluessigkeiten> Mechanik, Festkörper und Flüssigkeiten Klasse 7 (35)<option class=level-1 value=messungen-im-stromkreis-elektromagnete> Messungen im Stromkreis, Elektromagnete Klasse 8 (26)<option class=level-1 value=physik-oberstufe> Physik Oberstufe (19)<option class=level-1 value=schall-laerm-licht-und-sehen> Schall, Lärm, Licht und sehen Klasse 6 (15)<option class=level-1 value=strahlenoptik-elektromagnetische-induktion> Strahlenoptik, elektromagnetische Induktion Klasse 9 (22)<option class=level-0 value=sonstiges>Sonstiges (8)<option class=level-0 value=techni>Technik (5)<option class=level-0 value=uebersichten>Übersichten (33)<option class=level-0 value=webdesign>Webdesign (12)<option class=level-1 value=css> CSS (6)<option class=level-1 value=html> HTML (10)<option class=level-1 value=webserver> Webserver (1)<option class=level-0 value=witze>Witze (27)</select><script type=text/ez-screx>(function(){var dropdown=document.getElementById('wp-block-categories-1');function onCatChange(){if(dropdown.options[dropdown.selectedIndex].value!==-1){location.href="https://123mathe.de/?"+dropdown.name+'='+dropdown.options[dropdown.selectedIndex].value;}} dropdown.onchange=onCatChange;})();</script></div></section></aside></div><div class="site-footer-above-section-2 site-footer-section site-footer-section-2"><div class="footer-widget-area widget-area site-footer-focus-item" data-section=section-footer-menu><div class=footer-bar-navigation><nav class="site-navigation ast-flex-grow-1 navigation-accessibility footer-navigation" id=footer-site-navigation aria-label="Website-Navigation: Footer Navigation" itemtype=https://schema.org/SiteNavigationElement itemscope><div class=footer-nav-wrap><ul id=astra-footer-menu class="ast-nav-menu ast-flex astra-footer-horizontal-menu astra-footer-tablet-horizontal-menu astra-footer-mobile-horizontal-menu"><li id=menu-item-18442 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-18442"><a href=https://123mathe.de/feedback class=menu-link>Feedback unserer Besucher</a><li id=menu-item-18443 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-18443"><a href=https://123mathe.de/kostenloses-dankeschoen class=menu-link>Kostenloses Dankeschön</a><li id=menu-item-18444 class="menu-item menu-item-type-custom menu-item-object-custom menu-item-18444"><a href=https://123mathe.de/witze-uebersicht class=menu-link>Witze</a><li id=menu-item-18445 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-18445"><a href=https://123mathe.de/impressum class=menu-link>Impressum</a><li id=menu-item-18446 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-18446"><a href=https://123mathe.de/datenschutzerklaerung class=menu-link>Datenschutzerklärung</a><li id=menu-item-23797 class="menu-item menu-item-type-post_type menu-item-object-post menu-item-23797"><a href=https://123mathe.de/allgemeine-geschaeftsbedingungen class=menu-link>Allgemeine Geschäftsbedingungen</a></ul></div></nav></div></div></div></div></div></div><div class="site-primary-footer-wrap ast-builder-grid-row-container site-footer-focus-item ast-builder-grid-row-full ast-builder-grid-row-tablet-full ast-builder-grid-row-mobile-full ast-footer-row-stack ast-footer-row-tablet-stack ast-footer-row-mobile-stack" data-section=section-primary-footer-builder><div class=ast-builder-grid-row-container-inner><div class="ast-builder-footer-grid-columns site-primary-footer-inner-wrap ast-builder-grid-row"><div class="site-footer-primary-section-1 site-footer-section site-footer-section-1"><aside class="footer-widget-area widget-area site-footer-focus-item footer-widget-area-inner" data-section=sidebar-widgets-footer-widget-3 aria-label="Footer Widget 3"><section id=block-27 class="widget widget_block"><h3 class=wp-block-heading id=h-neueste-beitrage>Neueste Beiträge</h3></section><section id=block-26 class="widget widget_block widget_recent_entries"><ul class="wp-block-latest-posts__list is-grid columns-3 wp-block-latest-posts has-medium-font-size"><li><a class=wp-block-latest-posts__post-title href=https://123mathe.de/allgemeine-geschaeftsbedingungen>Allgemeine Geschäftsbedingungen</a><li><a class=wp-block-latest-posts__post-title href=https://123mathe.de/uebersicht-physik-sekundarstufe-i>Übersicht Physik Sekundarstufe I</a><li><div class=wp-block-latest-posts__featured-image><a href=https://123mathe.de/aufgaben-zu-tangente aria-label="Aufgaben und Lösungen zur Tangente"><img loading=lazy decoding=async width=300 height=257 src="data:image/svg+xml,%3Csvg%20xmlns=%22http://www.w3.org/2000/svg%22%20width=%22313%22%20height=%22258%22%3E%3C/svg%3E" class="ezlazyload attachment-medium size-medium wp-post-image" alt style=max-height:200px data-ezsrc=https://123mathe.de/wp-content/uploads/2024/02/01_mc_l-300x257.gif></a></div><a class=wp-block-latest-posts__post-title href=https://123mathe.de/aufgaben-zu-tangente>Aufgaben und Lösungen zur Tangente</a></ul></section></aside></div></div></div></div><div class="site-below-footer-wrap ast-builder-grid-row-container site-footer-focus-item ast-builder-grid-row-full ast-builder-grid-row-tablet-full ast-builder-grid-row-mobile-full ast-footer-row-stack ast-footer-row-tablet-stack ast-footer-row-mobile-stack" data-section=section-below-footer-builder><div class=ast-builder-grid-row-container-inner><div class="ast-builder-footer-grid-columns site-below-footer-inner-wrap ast-builder-grid-row"><div class="site-footer-below-section-1 site-footer-section site-footer-section-1"><div class="ast-builder-layout-element ast-flex site-footer-focus-item ast-footer-copyright" data-section=section-footer-builder><div class=ast-footer-copyright><div class="widget widget_block"><div class=widget-content><h3>Hier findest du unsere <a href=https://123mathe.de/humix/>📽️ Videos</a>.<br>Neue Beiträge kündigen wir auf <a href=https://www.facebook.com/123mathe>unserer Facebookseite</a> an.</h3><p>Die Unterrichtsmaterialien zu Mathematik, Physik und Gerätekunde stehen auf dieser Webseite kostenlos zur Verfügung.<p>Lehrer können <a href=https://123mathe.de/pdf-und-word-dateien>hier</a> Pakete mit <strong>WORD-Dateien</strong> kaufen, um individuelle Unterlagen zusammenzustellen.<p>Hier findet ihr unsere <a href=https://123mathe.de/allgemeine-geschaeftsbedingungen>Allgemeinen Geschäftsbedingungen.</a></div></div><p style=text-align:center>Copyright © 2025 123mathe | Powered by Wordpress</div></div></div></div></div></div></footer></div><div class="progress-wrap btn-left-side"><svg class="progress-circle" width="100%" height="100%" viewBox="-2 -2 104 104"> <path d="M50,1 a49,49 0 0,1 0,98 a49,49 0 0,1 0,-98"></path> </svg></div><script type=text/ez-screx>var offset=50;var duration=500;ezoicSiteSpeed(null,String(/windowLoad/).substring(1).slice(0,-1),String(/jQuery-window-load/).substring(1).slice(0,-1),function(){jQuery(window).on('scroll',function(){if(jQuery(this).scrollTop()>offset){jQuery('.progress-wrap').addClass('active-progress');}else{jQuery('.progress-wrap').removeClass('active-progress');}});jQuery('.progress-wrap').on('click',function(e){e.preventDefault();jQuery('html, body').animate({scrollTop:0},duration);return false;})})</script><script id=astra-theme-js-js-extra>var astra={"break_point":"921","isRtl":"","is_scroll_to_id":"","is_scroll_to_top":"","is_header_footer_builder_active":"1","responsive_cart_click":"flyout"};</script><script src="https://123mathe.de/wp-content/themes/astra/assets/js/minified/frontend.min.js?ver=4.8.12" id=astra-theme-js-js></script><script src="https://123mathe.de/wp-content/plugins/smooth-back-to-top-button/assets/js/smooth-back-to-top-button.js?screx=1&sxcb=10a&ver=1.1.14" id=sbttb-script-js type=text/ez-screx></script><script type=text/ez-screx>/(trident|msie)/i.test(navigator.userAgent)&&document.getElementById&&window.addEventListener&&window.addEventListener("hashchange",function(){var t,e=location.hash.substring(1);/^[A-z0-9_-]+$/.test(e)&&(t=document.getElementById(e))&&(/^(?:a|select|input|button|textarea)$/i.test(t.tagName)||(t.tabIndex=-1),t.focus())},!1);</script><img src=https://vg06.met.vgwort.de/na/365997b1ca2d4637862204a55f7764c3 width=1 height=1 alt class=wpvgw-marker-image loading=eager data-no-lazy=1 referrerpolicy=no-referrer-when-downgrade style=display:none ezimgfmt="rs rscb10 src ng ngcb10"> <script data-cfasync=false>!function(){var e=function(e,t){for(var r=0;r<t.length;r++){var n=t[r];if(0==n.complete||void 0!==n.readyState&&n.readyState<4){var o=n.getAttribute("src")||n.currentSrc;void 0!==n.readyState&&0==n.readyState?n.addEventListener("loadstart",(function(e){var t=e.currentTarget.getAttribute("src")||e.currentSrc;window.ezorqs(e,t)})):(o=n.getAttribute("src")||n.currentSrc,window.ezorqs(n,o)),n.addEventListener("load",(function(e){var t=e.currentTarget.getAttribute("src")||e.srcElement.currentSrc;window.ezorqe(e,t)})),n.addEventListener("loadeddata",(function(e){var t=e.currentTarget.getAttribute("src")||e.srcElement.currentSrc;window.ezorqe(e,t)})),n.addEventListener("error",(function(e){var t=e.currentTarget.getAttribute("src")||e.srcElement.currentSrc;window.ezorqe(e,t)}))}}};function t(e){for(var t=0;t<document.styleSheets.length;t++)if(document.styleSheets[t].href==e)return!0;return!1}__ez_addAllListeners=function(){e(0,document.querySelectorAll("img")),e(0,document.querySelectorAll("video")),e(0,document.querySelectorAll("audio")),function(e){for(var r=0;r<e.length;r++){var n=e[r];if(("preload"==n.getAttribute("rel")||"stylesheet"==n.getAttribute("rel"))&&null!=n.getAttribute("href")&&t(n.getAttribute("href"))){window.ezorqs(n,n.getAttribute("href"));var o=document.createElement("img");o.onerror=function(e){void 0!==e.path&&void 0!==e.path[0].currentSrc?window.ezorqe(n,e.path[0].currentSrc):void 0!==e.srcElement&&void 0!==e.srcElement.href&&window.ezorqe(n,e.srcElement.href)},o.src=n.getAttribute("href")}}}(document.querySelectorAll("link")),void 0!==window.__ez.ssaf&&window.__ez.ssaf.indexOf(16)>-1&&void 0!==window.__ez.sshsdef&&!1===window.__ez.sshsdef&&Element.prototype.addEventListener&&("function"==typeof window.onload&&(window.addEventListener("load",window.onload),window.onload=null),"function"==typeof document.onload&&(document.addEventListener.addEventListener("load",document.onload),document.onload=null))},__ez.queue.addFunc("__ez_addAllListeners","__ez_addAllListeners",null,!1,["/detroitchicago/tulsa.js"],!0,!0,!0,!0)}();</script><script data-cfasync=false>__ez.queue.addFile('/tardisrocinante/script_delay.js','/tardisrocinante/script_delay.js?gcb=4&cb=2',false,['/tardisrocinante/screx.js'],true,false,true,false);</script><script data-cfasync="false">function _emitEzConsentEvent(){var customEvent=new CustomEvent("ezConsentEvent",{detail:{ezTcfConsent:window.ezTcfConsent},bubbles:true,cancelable:true,});document.dispatchEvent(customEvent);} (function(window,document){function _setAllEzConsentTrue(){window.ezTcfConsent.loaded=true;window.ezTcfConsent.store_info=true;window.ezTcfConsent.develop_and_improve_services=true;window.ezTcfConsent.measure_ad_performance=true;window.ezTcfConsent.measure_content_performance=true;window.ezTcfConsent.select_basic_ads=true;window.ezTcfConsent.create_ad_profile=true;window.ezTcfConsent.select_personalized_ads=true;window.ezTcfConsent.create_content_profile=true;window.ezTcfConsent.select_personalized_content=true;window.ezTcfConsent.understand_audiences=true;window.ezTcfConsent.use_limited_data_to_select_content=true;window.ezTcfConsent.select_personalized_content=true;} function _clearEzConsentCookie(){document.cookie="ezCMPCookieConsent=tcf2;Domain=.123mathe.de;Path=/;expires=Thu, 01 Jan 1970 00:00:00 GMT";} _clearEzConsentCookie();if(typeof window.__tcfapi!=="undefined"){window.ezgconsent=false;var amazonHasRun=false;function _ezAllowed(tcdata,purpose){return(tcdata.purpose.consents[purpose]||tcdata.purpose.legitimateInterests[purpose]);} function _handleConsentDecision(tcdata){window.ezTcfConsent.loaded=true;if(!tcdata.vendor.consents["347"]&&!tcdata.vendor.legitimateInterests["347"]){window._emitEzConsentEvent();return;} window.ezTcfConsent.store_info=_ezAllowed(tcdata,"1");window.ezTcfConsent.develop_and_improve_services=_ezAllowed(tcdata,"10");window.ezTcfConsent.measure_content_performance=_ezAllowed(tcdata,"8");window.ezTcfConsent.select_basic_ads=_ezAllowed(tcdata,"2");window.ezTcfConsent.create_ad_profile=_ezAllowed(tcdata,"3");window.ezTcfConsent.select_personalized_ads=_ezAllowed(tcdata,"4");window.ezTcfConsent.create_content_profile=_ezAllowed(tcdata,"5");window.ezTcfConsent.measure_ad_performance=_ezAllowed(tcdata,"7");window.ezTcfConsent.use_limited_data_to_select_content=_ezAllowed(tcdata,"11");window.ezTcfConsent.select_personalized_content=_ezAllowed(tcdata,"6");window.ezTcfConsent.understand_audiences=_ezAllowed(tcdata,"9");window._emitEzConsentEvent();} function _handleGoogleConsentV2(tcdata){if(!tcdata||!tcdata.purpose||!tcdata.purpose.consents){return;} var googConsentV2={};if(tcdata.purpose.consents[1]){googConsentV2.ad_storage='granted';googConsentV2.analytics_storage='granted';} if(tcdata.purpose.consents[3]&&tcdata.purpose.consents[4]){googConsentV2.ad_personalization='granted';} if(tcdata.purpose.consents[1]&&tcdata.purpose.consents[7]){googConsentV2.ad_user_data='granted';} if(googConsentV2.analytics_storage=='denied'){gtag('set','url_passthrough',true);} gtag('consent','update',googConsentV2);} __tcfapi("addEventListener",2,function(tcdata,success){if(!success||!tcdata){window._emitEzConsentEvent();return;} if(!tcdata.gdprApplies){_setAllEzConsentTrue();window._emitEzConsentEvent();return;} if(tcdata.eventStatus==="useractioncomplete"||tcdata.eventStatus==="tcloaded"){if(typeof gtag!='undefined'){_handleGoogleConsentV2(tcdata);} _handleConsentDecision(tcdata);if(tcdata.purpose.consents["1"]===true&&tcdata.vendor.consents["755"]!==false){window.ezgconsent=true;(adsbygoogle=window.adsbygoogle||[]).pauseAdRequests=0;} if(window.__ezconsent){__ezconsent.setEzoicConsentSettings(ezConsentCategories);} __tcfapi("removeEventListener",2,function(success){return null;},tcdata.listenerId);if(!(tcdata.purpose.consents["1"]===true&&_ezAllowed(tcdata,"2")&&_ezAllowed(tcdata,"3")&&_ezAllowed(tcdata,"4"))){if(typeof __ez=="object"&&typeof __ez.bit=="object"&&typeof window["_ezaq"]=="object"&&typeof window["_ezaq"]["page_view_id"]=="string"){__ez.bit.Add(window["_ezaq"]["page_view_id"],[new __ezDotData("non_personalized_ads",true),]);}}}});}else{_setAllEzConsentTrue();window._emitEzConsentEvent();}})(window,document);</script></body></html>