Shadow_Messiah19
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I have a weird proof by contradiction question that I can't seem to find an answer for anywhere.

A is rational, B is irrational. Prove by contradiction A-B is irrational.
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RDKGames
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(Original post by Shadow_Messiah19)
I have a weird proof by contradiction question that I can't seem to find an answer for anywhere.

A is rational, B is irrational. Prove by contradiction A-B is irrational.
Suppose A-B is rational. Then it can be written in the form A-B = \dfrac{p}{q} where p \in \mathbb{Z} and q \in \mathbb{N}.

Now, you know that A is rational. Express it as \dfrac{r}{s}. So can you tell me what the problem is with B= \dfrac{r}{s}- \dfrac{p}{q} ??
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Shadow_Messiah19
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(Original post by RDKGames)
Suppose A-B is rational. Then it can be written in the form A-B = \dfrac{p}{q} where p \in \mathbb{Z} and q \in \mathbb{N}.

Now, you know that A is rational. Express it as \dfrac{r}{s}. So can you tell me what the problem is with B= \dfrac{r}{s}- \dfrac{p}{q} ??
I honestly don't know.. Maybe when you cross multiply it ends up proving B is rational? So that's a contradiction?
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RDKGames
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(Original post by Shadow_Messiah19)
I honestly don't know.. Maybe when you cross multiply it ends up proving B is rational? So that's a contradiction?
exactly
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