Multiplication of Natural Numbers proof

Quote:

Originally Posted by jstarks44444

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 $mn~?$