$x \mapsto \sin(1/x)$ on $(0, \infty)$

Example · Undergraduate

Terms

Term	This example	Why
continuous	✓	$x \mapsto \sin(1/x)$ is continuous on $(0, \infty)$.
uniformly continuous	✗	$x \mapsto \sin(1/x)$ is not uniformly continuous, because it oscillates between $-1$ and $1$ faster and faster as $x \to 0$.

Distinctions using this example

• Continuous vs. uniformly continuous

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