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**Least Upper Bound proof....**

## Homework Statement

Suppose A is a nonempty set that has x as an upper bound. Prove that x is the least upper bound of the set A iff for any E>0 there exists a y in A such that y>x-E

## Homework Equations

None

## The Attempt at a Solution

The forward where you assume that x is the least upper bound is very easy, but I'm having some trouble proving the reverse.....

This is what I have so far....

Let x be an upper bound of A, and choose a point z in A.

If x is an upper bound of A, then x+z is also an upper bound.