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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]].
[[Kurt Godel]] ended the grand ambition of set theory in 1931 by showing that no one can ever prove that mathematics is entirely consistent (i.e., without internal contradiction) or complete (i.e., all math statements can be proven true or false).
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.
[[Category: set theory]]
[[Category: set theory]]