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Needs:
Real Arithmetic ›
Needed by:
None.
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Periodic Functions

Why

We want to discuss a function which repeats itself on regular intervals.1

Definition

A function $f: \R \to \R $ is periodic with period $\alpha \in \R $ if

\[ f(x + \alpha ) = f(x) \]

for all $x \in \R $. In this case we call $f$ $\alpha $-periodic.

  1. Future editions will introduce this after the functions $\sin$, $\cos$, etc. ↩︎
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