Membership (set theory)

In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.

Writing ${\displaystyle A=\{1,2,3,4\}}$ means that the elements of the set A are the numbers 1, 2, 3 and 4. Sets of elements of A, for example ${\displaystyle \{1,2\}}$, are subsets of A.

Sets can themselves be elements. For example, consider the set ${\displaystyle B=\{1,2,\{3,4\}\}}$. The elements of B are not 1, 2, 3, and 4. Rather, there are only three elements of B, namely the numbers 1 and 2, and the set ${\displaystyle \{3,4\}}$.

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