# Foundations Proof of x^2n beeing even and other fundamental proofs

1. Dec 19, 2015

### moriheru

Is there a book containing fundamental proofs such as any number of the form x^2n beeing even and such.
I know this is very vague, so I must apologize.
Thanks for any help.

2. Dec 19, 2015

### andrewkirk

What sort of proofs did you have in mind? x^2n ($x^{2n}$)is not necessarily even. It is always odd for x odd, so there is no proof of it.

3. Dec 20, 2015

### moriheru

Sorry I meant a proof concerning all numbers with a even exponent beeing positive and vice versa.

4. Dec 22, 2015

### SrVishi

To add in my two cents, this sounds like something you may find in a "transition to mathematics" book. I'm pretty sure at least some of them conatin many proofs like what you displayed above. If you can't acquire such books, it may be a great habit to, when encountering something like your theorem that powers of even numbers being even functions, tryproving it on your own first, and then look up a proof online, say proofwiki.

5. Dec 22, 2015