\begin{definition}[Definition:Element/Also known as]
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.
\end{definition}