# Thread: Multiplication of Natural Numbers proof

1. ## 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!

2. 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 $\displaystyle \mathbb{N}$ you posted before.
Suppose that $\displaystyle n\notin\mathbb{N}$
Based on the given we know that $\displaystyle n\in \mathbb{Z}$ so from the axiom $\displaystyle n=0\text{ or }-n\in \mathbb{N}$.
You have proven that $\displaystyle j>0$ for all $\displaystyle j\in\mathbb{N}$.
What would that say about $\displaystyle mn~?$