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Math Help - Proof by Induction

  1. #1
    mx-
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    Proof by Induction

    I need to prove the following axiom for addition:

    x + ( y + z ) = (x + y) + z /* associative */

    using proof by induction, I know I have to first prove using a base case followed by the inductive step.

    The only problem is its been a while and can't remember how to do the base case.

    Any help would be appreciated greatly.
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  2. #2
    MHF Contributor

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    Quote Originally Posted by mx- View Post
    I need to prove the following axiom for addition:

    x + ( y + z ) = (x + y) + z /* associative */

    using proof by induction, I know I have to first prove using a base case followed by the inductive step.

    The only problem is its been a while and can't remember how to do the base case.

    Any hlp would be appreciated greatly.
    That would depend upon exactly what it is you are trying to prove. I would be inclined to use two separate inductions:
    1) prove, by induction on y, that (x+ y)+ 1= x+ (y+ 1) for all x.

    2) prove, by induction on z, that (x+ y)+ z= x+ (y+ z) for all x and z using (1) as your base case.
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