Definition of the set membership symbol (2024)

The symbol $\in$ indicates set membership and means “is an element of” so that the statement $x \in A$ means that $x$ is an element of the set $A$. In other words, $x$ is one of the objects in the collection of (possibly many) objects in the set $A$.

For example, if $A$ is the set $\{ \diamondsuit, \heartsuit, \clubsuit, \spadesuit \}$, then $\heartsuit \in A$ but $\triangle \notin A$ (where the symbol $\notin$ means “not an element of”). Or if $I$ is the interval $[1,2]$, then $x \in I$ means $x$ is some real number in that interval, i.e., $x$ satisfies $1 \le x \le 2$.