Lebl-Basic-Analysis-I · Problem 1.3.4

Real Numbers

Mathematics · bounded-functions

Problem

Finish the proof of Proposition 1.3.7. That is, prove that given a set

D

, and two bounded functions

f : D \to \mathbb{R}

and

g : D \to \mathbb{R}

such that

f(x) \leq g(x)

for all

x \in D

, then

\inf_{x \in D} f(x) \leq \inf_{x \in D} g(x).