http://wiki.karljones.com/index.php?action=history&feed=atom&title=Russell%27s_Paradox 2026-10-23T17:50:21Z Revision history for this page on the wiki MediaWiki 1.24.2 http://wiki.karljones.com/index.php?title=Russell%27s_Paradox&diff=16547&oldid=prev 2016-08-17T17:24:15Z

<p>Created page with &quot;In the foundations of mathematics, &#039;&#039;&#039;Russell&#039;s paradox&#039;&#039;&#039; (also known as &#039;&#039;&#039;Russell&#039;s antinomy&#039;&#039;&#039;), discovered by <a href="/index.php/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a> in 1901, showed that some attempted for...&quot;</p> <p><b>New page</b></p><div>In the foundations of mathematics, '''Russell's paradox''' (also known as '''Russell's antinomy'''), discovered by [[Bertrand Russell]] in 1901, showed that some attempted formalizations of the [[naive set theory]] created by [[Georg Cantor]] led to a contradiction.<br /> <br /> The same paradox had been discovered a year before by Ernst Zermelo but he did not publish the idea, which remained known only to Hilbert, Husserl, and other members of the University of Göttingen.<br /> <br /> == Description ==<br /> <br /> According to naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves.<br /> <br /> If R is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set of all sets that are not members of themselves.<br /> <br /> == See also ==<br /> <br /> * [[Georg Cantor]]<br /> * [[Naive set theory]]<br /> <br /> == External links ==<br /> <br /> * [https://en.wikipedia.org/wiki/Russell%27s_paradox Russell's paradox] @ Wikipedia<br /> <br /> [[Category:Mathematics]]</div>

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