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 towards the end of the 19th
century that just doing "the obvious thing" with sets led to
embarrassing {paradox}es, 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 Fr�nkel set theory}.
{The beginnings of set theory
(http://www-groups.dcs.st-and.ac.uk/~history/HistoryTopics.html)}.
(1995-05-10)