set theory

set theory
—n
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

set theory definition

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