- #1

- 1

- 0

## Homework Statement

If S = { 1/n - 1/m | n, m [tex]\in[/tex] N}, find inf(S) and sup(S)

I'm having a really hard time wrapping my head around the proper way to tackle sumpremum and infimum problems. I've included the little that I've done thus far, I just need a nudge in the right direction. Correct me if I'm wrong but I gather that there are basically 2 ways to tackle these problems.

1. An "epsilon" argument using the definition of supremum/infimum

2. An argument using some variation of the archimedean property

## Homework Equations

N/A

## The Attempt at a Solution

S is bounded above by 1. Therefore, S has a supremum. Let u = sup(s). We know that u <= 1. We will show that u = 1 by proving that u cannot be less than 1.

Assume u < 1.

1/n - 1/m <= u < 1

Where do I go from here? Thanks.