Cantor's Set

set-theory

Definition

Cantor's Set

According to Cantor, a set $M$ is a collection into a whole of definite, distinct objects $m$ of intuition or thought. These objects are called the elements of $M$, with membership written

$$m\in M.$$

The essential idea is that the collection is treated as one object—a whole—rather than merely as a multiplicity. This is an intuitive characterisation, not an axiomatic definition.