Definition:Symmetric Set/Real Numbers

Definition
Let $\R$ be the set of real numbers.

Let $S \subseteq \R$ such that:
 * $\forall x \in S: -x \in S$

That is, for every element in $S$, its negative is also in $S$.

Then $S$ is a symmetric subset of $\R$, or (if $\R$ is implicit) $S$ is a symmetric set.

Also see

 * Definition:Symmetric Set: the definition for a general group, which can be seen to be compatible with this by way of Real Numbers under Addition form Abelian Group.