Thread: 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.

Originally Posted by mx-

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.