# Thread: [SOLVED] Proof question 3

1. ## [SOLVED] Proof question 3

Suppose n,B e N, where n > 0. SHow that if B^n = 0, then B = 0.

Im trying to do a proof by contradicion by assuming that B != 0, but I don't know where to go from there. Any advice...Thanks.

2. Originally Posted by jzellt
Suppose n,B e N, where n > 0. SHow that if B^n = 0, then B = 0.

Im trying to do a proof by contradicion by assuming that B != 0, but I don't know where to go from there. Any advice...Thanks.
I would recommend a proof by induction on n combined with contradiction to prove the induction step.

If n= 1 B^1= 0 gives immediately B= 0. Suppose that, for some k, B^k= 0 implies that B= 0, then if B^(k+1)= 0 and B is NOT 0, then we can divide both sides by B to get B^k= 0, which implies B= 0, a contradiction.