Basic Analysis I — Real Analysis · Problem 3.1.7

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · limits-of-functions

Problem

Find an example of a function

f : [-1, 1] \to \mathbb{R}

, where for

A := [0, 1]

, we have

f|_A(x) \to 0

x \to 0

, but the limit of

f(x)

x \to 0

does not exist. Note why you cannot apply Proposition 3.1.15.