= Fundamental period of a function
{title2=$T_0=\min\{T>0:f(x+T)=f(x)\ \forall x\}$}
= Fundamental period
{synonym}
The fundamental period is the least positive <period of a function>, when one exists. For $f(x)=\sin(2\pi x)$ it is one; for $f(x)=\sin^2(2\pi x)$ it is $1/2$. A <periodic function> need not have a fundamental period: a <constant function> has every positive period, and <periodic function without a least positive period> is a <nonconstant> exception. Every <nonconstant> <real-valued function> that is <continuous> and <periodic> on the <real line> does have a least positive period.
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