- #1

silvermane

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**Prove the supremum exists :)**

## Homework Statement

Let A = {x:x in Q, x^3 < 2}.

Prove that sup A exists. Guess the value of sup A.

## The Attempt at a Solution

First we show that it is non-empty. We see that there is an element, 1 in the set, thus A is non-empty.

Now we show that A is bounded. We see that 2 is not in the set, thus there must be an upper bound on our set. Our set can be represented as (-oo, 2).

Since A is bounded above, then supA exists, and we are done.

(I just need help clarifying and making sure that I am following the correct logic here.)

=)

Also, would supA = 2?

Thanks for all your help in advance