Basic Analysis I — Real Analysis · Problem 3.3.13

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · extreme-and-intermediate-value-theorems

Problem

True/False, prove or find a counterexample. If

f : \mathbb{R} \to \mathbb{R}

is a continuous function such that

f|_{\mathbb{Z}}

is bounded, then

f

is bounded.