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Zero Divided By Some Integer n

  1. Jul 23, 2014 #1
    I tried to prove this claim, as I require it to finish one of my proofs.

    By definition, if a,b are integers, with [itex]a \ne 0[/itex], 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?
  2. jcsd
  3. Jul 23, 2014 #2
    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.
  4. Jul 23, 2014 #3
    Oh, whoops. I always seem to write it backwards. Thanks, I see now!
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