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Discrete Math: Functions with Powers

  1. Dec 5, 2011 #1
    Did this as a hw problem, got it wrong obviously. Not too sure how to solve it otherwise

    1. The problem statement, all variables and given/known data
    Let f be a function from A to A. Prove that for all m,n ε N, f^m*f^n = f^(m+N)


    2. Relevant equations



    3. The attempt at a solution

    f^(m+1) f^(n+1) = f(f^m) * f(f^n)
    = f(f^m * f^n) <--- this I think is what I did wrong
    = f(f^(m+n)) since a^m * a^n = a^(m+n)
    = f^(m+n+1)
    = f^(x+1) where x = m+n
     
  2. jcsd
  3. Dec 5, 2011 #2
    Can't find edit button:
    Found an error.. it should say
    1. The problem statement, all variables and given/known data
    Let f be a function from A to A. Prove that for all m,n ε N, f^m*f^n = f^(m+n)
     
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