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## Homework Statement

Prove that if

(i) [tex]\forall n[/tex][tex]\in N[/tex], u - (1/n) is not an upper bound of s

(ii) [tex]\forall n[/tex][tex]\in N[/tex], u + (1/n) is an upper bound of S

then, u = supS

## Homework Equations

## The Attempt at a Solution

It (i) and (ii) are true, then

[tex]\exists s[/tex][tex]\in S[/tex] s.t. u - (1/n) < s

and u+(1/n)>s for all s.

I'm not sure where to go from here.