Symmetric set

In mathematics, a nonempty subset S of a group G is said to be symmetric if

where ${\displaystyle S^{-1}=\{x^{-1}:x\in S\}}$. In other words, S is symmetric if ${\displaystyle x^{-1}\in S}$ whenever ${\displaystyle x\in S}$.

If S is a subset of a vector space, then S is said to be symmetric if it is symmetric with respect to the additive group structure of the vector space; that is, if ${\displaystyle S=-S=\{-x:x\in S\}}$.

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