how would you prove by contradiction that if n is even then n^2 is even??

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- Jan 5th 2009, 01:42 AMhmmmmproof by contradiction
how would you prove by contradiction that if n is even then n^2 is even??

- Jan 5th 2009, 01:57 AMcraig
To prove by contradiction you assume the opposite of what is stated, ie that $\displaystyle n^2$ is odd.

As you are starting with an even number, then instead of $\displaystyle n$, lets use $\displaystyle 2n$.

$\displaystyle (2n)^2 = 4N$, therefore if $\displaystyle n \in Z$(intergers), $\displaystyle n^2$ is always even.

This is how I would do it anyway, I am sure there are different methods out there.

Craig (Happy)

ps does anyone know how to do the 'member of' sign in your maths formatting thing?

**Edit:**solved ;) - Jan 5th 2009, 04:12 AMLast_Singularity
- Jan 5th 2009, 04:35 AMChop Suey