Zero Divided By Some Integer n

[Bashyboy]

I tried to prove this claim, as I require it to finish one of my proofs.

By definition, if a,b are integers, with $a \ne 0$, we say that a divides b if there exists an integer c such that b = ca.

So, n divides 0 means that there exists some integer c such that n = c*0 = 0. But this would contradict the fact that n can't be zero.

What is wrong with this proof?

 

[slider142]

According to your definition, "n divides 0" means there is some integer c such that 0 = c*n. This differs from what you have written above.

 

[Bashyboy]

Oh, whoops. I always seem to write it backwards. Thanks, I see now!