$x \mapsto \sin(x)$ on $\reals$

Example · High school

Terms

Term	This example	Why
continuous	✓
uniformly continuous	✓	$\sin$ is uniformly continuous, and so continuous, because $\abs{\sin(x) - \sin(y)} \leq \abs{x - y}$, so the choice $\delta = \varepsilon$ works everywhere.

Distinctions using this example

• Continuous vs. uniformly continuous

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