Re:Things I Learned from a Job Hunt for a Senior Engineering...
by greenleafjacob on Wednesday April 25, 2018 @02:51AM
(#16919088)
Here's the proof from Baby Rudin:
> We now show that the equation (1) p^2=2 is not satisfied by any rational p. If there were such a p, we could write p=m/n where m and n are integers that are not both even. Let us assume this is done. Then (1) implies (2) m^2=2n^2. This shows m^2 is even. Hence m is even (if m were odd, m^2 would be odd), and so m^2 is divisible by 4. It follows that the right side of (2) is divisible by 4, so that n^2 is even, which implies that n is even.
> The assumption that (1) holds leads to the conclusion that both m and n are even, contrary to our choice of m and n. Hence (1) is impossible for rational p.
> We now show that the equation (1) p^2=2 is not satisfied by any rational p. If there were such a p, we could write p=m/n where m and n are integers that are not both even. Let us assume this is done. Then (1) implies (2) m^2=2n^2. This shows m^2 is even. Hence m is even (if m were odd, m^2 would be odd), and so m^2 is divisible by 4. It follows that the right side of (2) is divisible by 4, so that n^2 is even, which implies that n is even. > The assumption that (1) holds leads to the conclusion that both m and n are even, contrary to our choice of m and n. Hence (1) is impossible for rational p.