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The <strong>and-operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/tannery.jules" title="Author Profile">Tannery, J.</a></div> <h2 class="title"> <strong>Introduction to the theory of functions of one variable. Second edition, completely reworked. Volume 1. Irrational numbers, sets, limits, elementary functions, derivatives. (Introduction 脿 la th茅orie des fonctions d’une variable. Deuxi猫me 茅dition enti猫rement refondue. Tome I. Nombres irrationnels, ensembles, limites, fonctions 茅l茅mentaires, d茅riv茅es.)</strong> <i>(French)</i> <a class="label nowrap" href="/35.0374.01">JFM 35.0374.01</a> </h2> <div class="source"> Paris: A. Hermann. IX u. 422 S. (1904). </div> <div class="abstract">Die Grunds盲tze, die den Verf. bei der Bearbeitung der neuen Auflage seiner 1886 erschienenen Einf眉hrung in die Theorie der Funktionen einer Ver盲nderlichen geleitet haben, hat er in der Vorrede selbst dargelegt. Die erste Auflage habe ihre Dienste geleistet; Verbesserungen im kleinen h盲tten keinen Zweck gehabt, und deshalb habe er das Werk fast ganz neu geschrieben.<br class="zbmathjax-paragraph"> Den Ausgangspunkt bildet wieder der Begriff der ganzen Zahl, von dem aus man sich zu dem Begriffe einer stetigen Gr枚脽e erhebt. Aber w盲hrend Tannery in der ersten Auflage, um den logischen Aufbau der Theorie ungest枚rt und rein hervortreten zu lassen, vielleicht auch, “um sich selbst in der 脺berzeugung zu best盲rken, die er dem Leser einpr盲gen wollte”, sich jeder geometrischen Redewendung, jeder geometrischen Figur enthalten hatte, hat er jetzt diese Scheu 眉berwunden: wenn man von den Zahlen spreche, d眉rfe man nicht so tun, als wisse man nichts vom Raume; man habe das Recht, sich bei einer logischen Darstellung der Analysis der Ausdr眉cke und Figuren der Geometrie zu bedienen, vorausgesetzt, da脽 man es nur verstehe, sie in die Sprache der Zahlen zu 眉bersetzen und die numerischen Eigenschaften, die die Figuren erl盲utern, logisch abzuleiten; die Raumanschauung, die bei der Entwicklung der Analysis eine so gro脽e Rolle gespielt hat, k枚nne so dazu dienen, uns “voranzuleuchten”.<br class="zbmathjax-paragraph"> Tannery begegnet sich in dieser Ansicht mit F. Klein und D. Hilbert. Diese bestreiten, da脽 nur die Begriffe der Analysis oder gar nur diejenigen der Arithmetik einer v枚llig strengen Behandlung f盲hig seien; eine so einseitige Auslegung der Forderung der Strenge f眉hre zu einer Ignorierung aller aus der Geometrie, Mechanik und Physik stammenden Begriffe, zu einer Unterbindung des Zuflusses von neuem Material aus der Au脽enwelt und schlie脽lich sogar in letzter Konsequenz zu einer Verwerfung der Begriffe des Kontinuums und der Irrationalzahl.<br class="zbmathjax-paragraph"> Ein zweiter Unterschied gegen die erste Auflage ist die Stellung, die die Mengenlehre erhalten hat. W盲hrend Tannery es damals nur gewagt hatte, sie fl眉chtig zu streifen, l盲脽t er jetzt ihre Bedeutung hervortreten, die ebenso fundamental ist wie die des Begriffes der Grenze.<br class="zbmathjax-paragraph"> In engem Zusammenhange mit den beiden soeben dargelegten Gesichtspunkten steht der Umstand, da脽 die Theorie der Irrationalzahlen, im Gegensatze zu der ersten Auflage, auf die Dedekind schon Schnitte gegr眉ndet wird.<br class="zbmathjax-paragraph"> Bis auf die Theorie des Integrals enth盲lt der erste Band ungef盲hr dasselbe wie die erste Auflage. In dem zweiten Bande soll die Integralrechnung behandelt und im Anschlu脽 daran eine Einf眉hrung in die Theorie der Funktionen einer komplexen Ver盲nderlichen gegeben werden.<div class="reviewer"> Reviewer: <a href="/authors/?q=St%C3%A4ckel">St盲ckel, Prof. (Hannover)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A2653546">Cited in <strong>2</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A2653546">Cited in <strong>7</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A26-01" title="MSC2020">26-01</a> </td> <td class="space"> Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions </td> </tr></table> </div><div class="keywords"> <h3>JFM Section:</h3><a href="/?q=ut%3A%22Siebenter+Abschnitt.+Funktionentheorie.+Kapitel+1.+Allgemeines."">Siebenter Abschnitt. Funktionentheorie. Kapitel 1. Allgemeines.</a></div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ASets">Sets</a>; <a href="/?q=ut%3Aintegers">integers</a>; <a href="/?q=ut%3Areal+numbers">real numbers</a>; <a href="/?q=ut%3Alimits">limits</a>; <a href="/?q=ut%3Acontinuity">continuity</a>; <a href="/?q=ut%3Aelementary+functions">elementary functions</a>; <a href="/?q=ut%3Adifferentiation">differentiation</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="JFM" data-itemname="JFM 35.0374.01" data-ciurl="" data-biburl="/bibtex/02653546.bib" data-amsurl="/amsrefs/02653546.bib" data-xmlurl="/xml/02653546.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/02653546.pdf" title="JFM 35.0374.01 as PDF">Review PDF</a> </div> <div class="fulltexts"> </div> <div class="sfx" style="float: right;"> </div> </div> </article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>