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In mathematics, a periodic function is a function that repeats its values after some definite period has been added to its independent variable. This property is called periodicity. Everyday examples are seen when the variable is time; for instance the hands of a clock or the phases of the moon show periodic behaviour. Periodic motion is motion in which the position(s) of the system are expressible as periodic functions, all with the same period. For a function on the real numbers or on the integers, that means that the entire graph can be formed from copies of one particular portion, repeated at regular intervals. More explicitly, a function f is periodic with period P greater than zero if for all values of x in the domain of f. An aperiodic function (non-periodic function) is one that has no such period P (not to be confused with an antiperiodic function (below) for which f(x + P) = -f(x) for some P).
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