Help Solve Analysis Problem: Showing α is a Cut & αα=β

[zmac]

Please help!
Here is a homework question that I need help starting!
It is a fact that the squares of the rational numbers are dense in the positive rational numbers, that is, for any r1,r2 in Q with 0< r1< r2, there exists p in Q with r1< p2<r2. Let β be a cut such that 0*< β. Let α be the subset of Q defined by α={p in Q: p< or =0 or p2 in β}. Use the abovementioned density of the squares of rationals to show that α is a cut and that αα=β.

ps How do I put mathematical notation here?

Any foresight you can give would be greatly appreciated!
Thanks

 

[AKG]

The usual questions: what have you tried, where are you stuck, what are the definitions, etc?

 

[SteveRives]

I am having a little trouble interpreting the question. By p2, do you mean p squared?

Thanks,

Steve