1. the branch of pure mathematics that deals with the nature and relations of sets;

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set theory n 1: the branch of pure mathematics that deals with the nature and relations of setsThe Free On-line Dictionary of Computing (18 March 2015):

set theoryA 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 (http://www-groups.dcs.st-and.ac.uk/~history/HistoryTopics.html). (1995-05-10)