Lebl-Basic-Analysis-I · Problem 1.2.16

Real Numbers

Mathematics · archimedean-property

Problem

Prove that if

A \subset \mathbb{Z}

is a nonempty subset bounded below, then there exists a least element in

A

. Now describe why this statement would simplify the proof of Theorem 1.2.4 part (ii) so that you do not have to assume

x \geq 0