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A periodic function is a function that repeats itself in regular intervals, ie, one satisfying $f(x+P)=f(x).$ Here, $P$ is the period.

Graphically, you can see periodicity through translational symmetry. You can see this most easily with trigonometric functions like $\sin$ and $\cos$, which have period $2\pi$. Another example of a periodic function is the nonlinear sawtooth function.

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