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One paradox in naive set theory was announced by [[Bertrand Russell]] in 1901, and is known as [[Russell's Paradox]].
One paradox in naive set theory was announced by [[Bertrand Russell]] in 1901, and is known as [[Russell's Paradox]].
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.
Like all sufficiently strong mathematical theories, set theory is incomplete, as shown by [[Kurt Gödel]]. 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.
==The Empty Set==
==The Empty Set==