Basic Analysis I — Real Analysis · Problem 1.2.16

Real Numbers — Jiri Lebl

Mathematics — Real Analysis · integers

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