Question

prove that If a least upper or a greatest lower bound for S exists, then it is unique.

Answer 1

What have you tried?

Answer 2

I'll sketch the idea for the uniqueness of the least upper bound. It's a similar idea for the greatest lower bound.

In order for s to be the least upper bound of a set S, s has to satisfy two properties.

1) For any \(x\in S\), \(x\le s\), and
2) If \(u\) is any upper bound of S, then \(s\le u\).

Assume you have two least upper bounds, \(s_1,s_2\). What happens if they both have the second property?

Answer 3

prove s1<s2 and s2< s1 , which leads to s1 =s2, right? My master @nerdguy2535 :)

Answer 4

yep, thats right :)