Basic Analysis I — Real Analysis · Problem 1.1.2

Real Numbers — Jiri Lebl

Mathematics — Real Analysis · ordered-sets

Problem

Let

S

be an ordered set. Let

A \subset S

be a nonempty finite subset. Then

A

is bounded. Furthermore,

\inf A

exists and is in

A

and

\sup A

exists and is in

A

. Hint: Use induction.