https://www.conservapedia.com/api.php?action=feedcontributions&feedformat=atom&user=Purify2glorify 2026-11-09T04:58:33Z User contributions MediaWiki 1.35.14 https://www.conservapedia.com/index.php?title=Set_theory&diff=807956 2010-08-19T23:29:46Z

<p>Purify2glorify: </p> <hr /> <div>'''Set theory''' is a branch of [[mathematics]] dealing with collections of objects. <br /> <br /> *The language of set theory is based on a single fundamental relation, called membership. We say that A is a member of B (in symbols A ∈ B), or that the set B contains A as its element. The understanding is that a set is determined by its elements; in other words, two sets are deemed equal if they have exactly the same elements. &lt;ref&gt;http://plato.stanford.edu/entries/set-theory/&lt;/ref&gt;<br /> <br /> ==History of set theory==<br /> <br /> It was developed in the late 1800s, primarly by the German mathematician [[Georg Cantor]]. This initial attempt became known as &quot;naive set theory&quot; because mathematicians found flaws in it. It was replaced by &quot;axiomatic set theory&quot; in the early 1900s. The most commonly used such axiomatization is [[Zermelo-Fraenkel]] set theory.<br /> <br /> One paradox in naive set theory was announced by [[Bertrand Russell]] in 1901, and is known as [[Russell's Paradox]].<br /> <br /> Like all sufficiently strong mathematical theories, set theory is incomplete, as shown by [[Kurt Godel]]. However, set theory is the received axiomatization of mathematics today, with subjects like analysis, [[algebra]], topology, and [[geometry]] using set theory and its language for their own foundation.<br /> <br /> ==The Empty Set==<br /> <br /> The empty set is the set with no members. Because sets are uniquely defined by membership, the empty set is unique. The empty set is usually denoted by {} or ∅.<br /> <br /> ==References==<br /> <br /> &lt;References/&gt;<br /> <br /> [[Category: set theory]]</div>

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