= Period group of a function
{title2=$\operatorname{Per}(f)=\{T\in\mathbb R:f(x+T)=f(x)\ \forall x\}$}
Include zero when forming this <set>, even though a <period of a function> is normally required to be nonzero. For $f:\mathbb R\to Y$, $\operatorname{Per}(f)$ is a <subgroup> of the <additive group> of the <real numbers>: composing two preserving shifts adds them, and reversing a preserving shift negates it. A <constant function> has period group $\mathbb R$. A <nonconstant> <continuous> <real-valued function> that is <periodic> has period group $T_0\mathbb Z$, where $T_0$ is its <fundamental period>.
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