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Naive set theory
In abstract mathematics, naive set theory was the first development of set theory, which was later to be framed more carefully as axiomatic set theory. Naive set theory is distinguished from axiomatic set theory by the fact that the former relies on an informal understanding of sets as collections of objects, called the elements or members of the set, whereas the latter uses only those facts about sets and membership provable from definite lists of axioms (derived from our understanding of collections of objects and their members, but framed with care for various purposes, including but not limited to avoiding the known paradoxes).
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