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.