Hello everyone,

I want to prove that for postive integers $\displaystyle x, y, x+y \ne y $. I want to do this using the WOP. Here's what I have done so far:

Suppose for some postive integer $\displaystyle x, \exists y $ such that $\displaystyle y=x+y$. By the WOP, there exists a smallest $\displaystyle x_0 $ such that $\displaystyle y=x_0+y$. Now I think I may have to apply the WOP again, but am not sure. Any advice?

Thanks a lot,

Kevin