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Math Help - Multiplication of Natural Numbers proof

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    Multiplication of Natural Numbers proof

    Let m be an element of the Natural Numbers and n be an element of the Integers. If m*n is an element of the Natural Numbers, then n is an element of the Natural Numbers.

    Any help with the above proof would be appreciated!
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    Quote Originally Posted by jstarks44444 View Post
    Let m be an element of the Natural Numbers and n be an element of the Integers. If m*n is an element of the Natural Numbers, then n is an element of the Natural Numbers.
    One again, if you would post a list of axioms, definitions, and theorems you would receive better help.

    Not having a such here a guess based upon the definition of \mathbb{N} you posted before.
    Suppose that n\notin\mathbb{N}
    Based on the given we know that n\in \mathbb{Z} so from the axiom n=0\text{ or }-n\in \mathbb{N}.
    You have proven that j>0 for all j\in\mathbb{N} .
    What would that say about mn~?
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