Definition:Element

Definition
An element is a member of a set.

We use the symbol $$x \in S$$ to mean $$x$$ is an element of the set $$S$$.

Similarly, $$x \notin S$$ means $$x$$ is not an element of $$S$$.

The symbol can be reversed:
 * $$S \ni x$$ means the set $$S$$ has $$x$$ as an element

but this is rarely seen.

Some texts (usually older ones) use $$x \ \overline \in \ S$$ instead of $$x \notin S$$.

The term member is sometimes used (probably more for the sake of linguistic variation than anything else).

In the context of geometry, elements of a set are often called points, in particular when they are (geometric) points.

Historical Note
The symbol originated as $$\varepsilon$$, first used by Giuseppe Peano in Arithmetices prinicipia nova methodo exposita (1889). It comes from the first letter of the Greek word meaning is.

The stylized version $$\in$$ was first used by Bertrand Russell in Principles of Mathematics in 1903.

$$x \ \varepsilon \ S$$ could still be seen in works as late as, but the symbol $$\in$$ is now practically universal.