When one always uses sets in mathematics, a set $S$ is thought to consist of certain distinct objects $x$ satisfying some known condition. Then we say that $x$ is a member or an element of the set $S$ (denoted $x \in S$ ). In the opposite case, when $x$ does not satisfy the condition, $x$ is not a member of $S$ (denoted $x \notin S$ ).

A member of a set belongs to this set. We may think that it is a question of a relation `to belong' between members and sets, the set-membership relation, having the notation ``$\in$ ''. It is the most fundamental concept of the set theory.

Example. We can speak of the set of the positive primes. If this set is $\mathbb{P}$ , then the condition defining the members of $\mathbb{P}$ is `to be a positive prime' and the list of the elements may be written $$2,\,3,\,5,\,7,\,11,\,\ldots$$ So we have e.g. $$11 \in \mathbb{P}, \quad 1\notin \mathbb{P}.$$