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

  1. Dec 19, 2015 #1
    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. jcsd
  3. Dec 19, 2015 #2


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    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.
  4. Dec 20, 2015 #3
    Sorry I meant a proof concerning all numbers with a even exponent beeing positive and vice versa.
  5. Dec 22, 2015 #4
    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.
  6. Dec 22, 2015 #5
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