set theory
<mathematics> A mathematical formalisation of the theory of "sets"
(aggregates or collections) of objects ("elements" or "members"). Many
mathematicians use set theory as the basis for all other mathematics.
Mathematicians began to realise toward the end of the 19th century that just
doing "the obvious thing" with sets led to embarrassing paradoxes, the most
famous being Russell's Paradox. As a result, they acknowledged the need for a
suitable axiomatisation for talking about sets. Numerous such axiomatisations
exist; the most popular among ordinary mathematicians is Zermelo Fränkel set
theory.
The beginnings of set theory.
(1995-05-10)
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