# Existence of Nonconstant Periodic Function with no Period

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## Theorem

There exists a real, non-constant function $f$ such that:

- $(1): \quad f$ is periodic.

- $(2): \quad f$ does
**not**have a period.

## Proof

By Dirichlet Function is Periodic and Dirichlet Function has no Period, it is seen that the Dirichlet functions are such an example.

$\blacksquare$