|Noun||1.||set theory - the branch of pure mathematics that deals with the nature and relations of sets|
|(mathematics)||set theory - 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.