Definition:Element/Also known as

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

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

$x \in S$ can also be read as:


 * $x$ is in $S$
 * $x$ belongs to $S$
 * $S$ includes $x$
 * $x$ is included in $S$
 * $S$ contains $x$

However, beware of this latter usage: $S$ contains $x$ can also be interpreted as $x$ is a subset of $S$. Such is the scope for misinterpretation that it is mandatory that further explanation is added to make it clear whether you mean subset or element.