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mw-hide-empty-elt ns-0 ns-subject mw-editable page-axiom_of_union rootpage-axiom_of_union skin-vector action-view"><div id="mw-page-base" class="noprint"></div> <div id="mw-head-base" class="noprint"></div> <div id="content" class="mw-body" role="main"> <a id="top"></a> <div id="siteNotice"></div> <div class="mw-indicators"> </div> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">axiom of union</span></h1> <div id="bodyContent" class="vector-body"> <div id="siteSub" class="noprint">From Wiktionary, the free dictionary</div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="contentSub2"></div> <div id="jump-to-nav"></div> <a class="mw-jump-link" href="#mw-head">Jump to navigation</a> <a class="mw-jump-link" href="#searchInput">Jump to search</a> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="mw-heading mw-heading2"><h2 id="English">English</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=axiom_of_union&action=edit&section=1" title="Edit section: English"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="interproject-box sister-wikipedia sister-project noprint floatright"><div style="float: left;"><figure class="mw-halign-none" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/44px-Wikipedia-logo-v2.svg.png" decoding="async" width="44" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/66px-Wikipedia-logo-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/88px-Wikipedia-logo-v2.svg.png 2x" data-file-width="103" data-file-height="94" /></span><figcaption></figcaption></figure></div><div style="margin-left: 60px;">English <a href="/wiki/Wikipedia" title="Wikipedia">Wikipedia</a> has an article on:<div style="margin-left: 10px;"><b class="Latn" lang="en"><a href="https://en.wikipedia.org/wiki/axiom_of_union" class="extiw" title="w:axiom of union">axiom of union</a></b></div></div><span class="interProject"><a href="https://en.wikipedia.org/wiki/axiom_of_union" class="extiw" title="w:axiom of union">Wikipedia </a></span></div><style data-mw-deduplicate="TemplateStyles:r81571951">.mw-parser-output .interproject-box{font-size:90%;width:250px;padding:4px;text-align:left;background:var(--wikt-palette-paleblue,#f9f9f9);border:var(--border-color-base,#aaa)1px solid}@media screen and (max-width:719px){.mw-parser-output .interproject-box{box-sizing:border-box;line-height:1.5;width:100%;max-width:100%}}</style> <div class="mw-heading mw-heading3"><h3 id="Noun">Noun</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=axiom_of_union&action=edit&section=2" title="Edit section: Noun"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="headword-line"><strong class="Latn headword" lang="en"><a href="/wiki/axiom#English" title="axiom">axiom</a> <a href="/wiki/of#English" title="of">of</a> <a href="/wiki/union#English" title="union">union</a></strong></span> </p> <ol><li><span class="usage-label-sense"><span class="ib-brac">(</span><span class="ib-content"><a href="/wiki/set_theory" title="set theory">set theory</a></span><span class="ib-brac">)</span></span> One of the axioms in <a href="/wiki/axiom" title="axiom">axiomatic</a> <a href="/wiki/set_theory" title="set theory">set theory</a>, equivalent to the statement that a <a href="/wiki/union" title="union">union</a> exists for any set, containing exactly all the elements contained within the sets within that set.</li></ol> <div class="mw-heading mw-heading4"><h4 id="Translations">Translations</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=axiom_of_union&action=edit&section=3" title="Edit section: Translations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="NavFrame" id="Translations-axiom_of_union"><div class="NavHead" style="text-align:left">axiom of union</div><div class="NavContent"><table class="translations" role="presentation" data-gloss="axiom of union"><tbody><tr><td class="translations-cell multicolumn-list" colspan="3"><style data-mw-deduplicate="TemplateStyles:r81584270">.mw-parser-output .translations{width:100%}.mw-parser-output .translations-cell{background-color:var(--wikt-palette-lightyellow,#FFFFe0);vertical-align:top;text-align:left}</style> <ul><li>Finnish: <span class="Latn" lang="fi"><a href="/w/index.php?title=yhdisteaksiooma&action=edit&redlink=1" class="new" title="yhdisteaksiooma (page does not exist)">yhdisteaksiooma</a></span></li> <li>German: <span class="Latn" lang="de"><a href="/w/index.php?title=Vereinigungsaxiom&action=edit&redlink=1" class="new" title="Vereinigungsaxiom (page does not exist)">Vereinigungsaxiom</a></span> <span class="gender"><abbr title="neuter gender">n</abbr></span></li> <li>Polish: <span class="Latn" lang="pl"><a href="/wiki/aksjomat#Polish" title="aksjomat">aksjomat</a> <a href="/wiki/suma#Polish" title="suma">sumy</a></span> <span class="gender"><abbr title="masculine gender">m</abbr></span></li></ul> </td></tr></tbody></table></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wiktionary.org/w/index.php?title=axiom_of_union&oldid=81984866">https://en.wiktionary.org/w/index.php?title=axiom_of_union&oldid=81984866</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div 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