(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that there is no upper bound in A, where A = {x in Q | x^{2}< 2}

3. The attempt at a solution

My attempt has been to assume that there is an upper bound p in A and then I have been trying to find a way to show that there is a number that is larger than p but still in A.

So I have tried doing some inequality expressions and saying that I need to find some x such that when I take the sum of p and x and square it, it is less than 2. [(p + x)^{2}< 2]

But in the end when I try to find this x using the just mentioned inequality statement I get that x is a number that is less than ((2 - p^{2}) / (2p + x)). So, this number is less than some expression that contains itself. I am having some trouble figuring this out.

So I need a q in Q, where q = p + x, and x is in Q+, and I need q^{2}< 2. That's about all I got so far.

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# Proving no upper bound in A, where A = {x in Q | x^2 < 2}

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