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 symbol $$\in$$ is a relatively modern styling of the Greek "epsilon".

Previous to its invention and widespread adoption, other "epsilon" variants (and their backwards forms) were often seen.


 * $$x \ \varepsilon \ S$$: used by: