$x \mapsto \sqrt{x}$ on $[0, \infty)$

Example · High school

Terms

Term	This example	Why
domain	$[0, \infty)$
continuous	✓
uniformly continuous	✓	$x \mapsto \sqrt{x}$ is uniformly continuous, and so continuous, because $\abs{\sqrt{x} - \sqrt{y}} \leq \sqrt{\abs{x - y}}$, so the choice $\delta = \varepsilon^2$ works everywhere.

Distinctions using this example

• Continuous vs. uniformly continuous

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