Talk:Natural Number Addition is Associative/Proof 2

Clearer proof
I think the proof should go as follows:

From the definition of addition, we have that:
 * x + 0 = x
 * x + y+ = (x + y)+

For any natural numbers x and y, (x + y) + 0 = x + y = x + (y + 0). For any natural number z, suppose that for all x and y, (x + y) + z = x + (y + z), then for all x and y, (x + y) + z+ = ((x + y) + z)+ = (x + (y + z))+ = x + (y + z)+ = x + (y + z+). By induction, for all x, y, and z, (x + y) + z = x + (y + z). Blackbombchu (talk) 03:47, 25 May 2015 (UTC)


 * User:Blackbombchu: Is there any difference? --kc_kennylau (talk) 05:50, 25 May 2015 (UTC)