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Math Help - Induction

  1. #1
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    Induction

    I'm supposed to prove this using induction. Any advice?

    let a be a real number. Prove by induction on n that a^(m+n) = (a^m)(a^n) for all positive integers m,n.

    Thanks for any advice.
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  2. #2
    Newbie
    Joined
    Dec 2007
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    i think it's ridiculous to use induction because

    a^(m+n) = aaaaaaaaa...aaaaa m+n times

    and a^(m)a^(n) = aaaa...aaa (m times) x aaaa....aaaa (n times)





    but if you used induction,

    a^(m+1) = aaaaa...aaaaa (m times) x a (1 time)

    and then if a^(m + n) = a^(m)a^(n), then

    a^(m + (n +1)) = a^((m + n) +1) = a^(m + n)a^(1) = a^(m)a^(n)a^(1) = a^(m)a^(n+1)


    sorry if it's confusing
    Last edited by jimmybuffet; March 5th 2008 at 10:19 PM.
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