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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.
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==
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 ∅.
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 ∅.