<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 FrÃ¤nkel set theory.