Hi everyone. I'm a math student still learning to do(adsbygoogle = window.adsbygoogle || []).push({});

proofs. Here is a problem I encountered that seems easy but

has me stuck.

1. The problem statement, all variables and given/known

data

Let a be a positive rational number. Let A = {x e Q (that

is, e is an element of the rationals) | x^2 < a}. Show that

A is bounded in Q. Find the least upper bound in R of this

set.

2. Relevant equations

None.

3. The attempt at a solution

So I want to show that there exists an M such that x < or =

to M for all x in A.

So for all x in A, x^2<a.

=> x < (a/x) if x>0 or x > (a/x) if x < 0

So it seems like I find an upper bound for x if x is

positive and a lower bound for x if x is negative but what

havn't acounted for the other cases.

Thanks for your help.

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# Homework Help: Show Set is Bounded

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