## Rational and Irrational Number Set proof.

Hello, here is my problem:

how can i prove that if $$a\in\mathbf{Q}$$ and $$t\in\mathbf{I}$$, then $$a+t\in\mathbf{I}$$ and $$at\in\mathbf{I}$$?

My original thought was to show that neither a+t or at can be belong to N, Z, or Q, thus they must belong to I. However i'm not certain if that train of thought is correct.

Also, i have a question that says given two irrational numbers s and t, what can be said about s+t and st.

My original thought he was that nothing can be shown, since it is possible to create numbers that belong to N, Z, Q, or I.

thanks for clarification.

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 Recognitions: Homework Help Science Advisor The rational numbers are a field. Oh, and I is not standard notation, by the way. As for the second one, then you can't say anythingabout s or t's rationality. Just construct some examples.
 whoa, thanks, i would have never gotten that.

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