1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.


    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


    User Avatar
    Staff Emeritus
    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Confusion with induction problem.
  1. Induction problems (Replies: 3)

  2. Induction problem (Replies: 7)

  3. Induction problem (Replies: 1)

  4. Problem on induction (Replies: 2)