Basic Analysis I — Real Analysis · Problem 3.4.8

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · uniform-continuity

Problem

Show that f:(0,∞)→Rf : (0, \infty) \to \mathbb{R} defined by f(x):=sin⁡(1/x)f(x) := \sin(1/x) is not uniformly continuous.

Related theory

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