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Homework Help: Confusion with induction problem.

  1. Dec 21, 2008 #1
    1. The problem statement, all variables and given/known data
    Let a in R and a != 0. Define a^0=1 and for all n in the positive integers, a^-n = 1/a^n.

    Show,

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

    (a^n)^m = a^nm

    a^m b^m =(ab)^m

    for all a,b != 0 and n,m in Z.


    3. The attempt at a solution

    Notice that last part where it says Z, not just N. I just proved these 3 laws using induction for n,m in N. I am confused now on how to approach the problem.

    Do I fix n, and let m = -1 for the base case. Then assume the statement is true to m<0 and show it is also true for m-1 ?

    Thank you for your time.

    EDIT: P35 in Munkres, Topology
     
    Last edited: Dec 21, 2008
  2. jcsd
  3. Dec 21, 2008 #2

    HallsofIvy

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    Science Advisor

    If you have proved that anam[/sup]= an+m for positive integers then you should be able to prove, in the same way, that a-na-m= a-n-m for m and n any positive integers.
     
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