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'sParadox. 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 Frankel set theory.

The beginnings of set theory.

(1995-05-10)