Lebl-Basic-Analysis-I · Problem 3.1.15

Continuous Functions

Mathematics · limits-of-functions

Problem

Show that the condition of being a cluster point is necessary to have a reasonable definition of a limit. That is, suppose

c

is not a cluster point of

S \subset \mathbb{R}

, and

f : S \to \mathbb{R}

is a function. Show that every

L

would satisfy the definition of limit at

c

without the condition on

c

being a cluster point.