set theory

the branch of mathematics that deals with relations between sets.

1940–45 Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
set theory
1.  maths the branch of mathematics concerned with the properties and interrelationships of sets
2.  logic a theory constructed within first-order logic that yields the mathematical theory of classes, esp one that distinguishes sets from proper classes as a means of avoiding certain paradoxes

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Computing Dictionary

set theory definition

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 (
The Free On-line Dictionary of Computing, © Denis Howe 2010
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Example sentences
One can describe the difference between constructs and concepts in terms of set theory.
In standard set theory, each element is either completely a member of a category or not a member at all.
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