Hello, here is my problem:(adsbygoogle = window.adsbygoogle || []).push({});

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

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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# Rational and Irrational Number Set proof.

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