# Thread: Proof of m > n in the Natural Numbers

1. ## Proof of m > n in the Natural Numbers

For each n in the Naturals there exists m in the Naturals such that m > n.

I'd really appreciate some help with the following proof. Thanks a bunch!

2. Originally Posted by jstarks44444
For each n in the Naturals there exists m in the Naturals such that m > n.

I'd really appreciate some help with the following proof. Thanks a bunch!

Simply take the succesor of n...
Tonio

3. Can you please explain this? I don't know how to word what you are saying.... do I just introduce n+1?

4. Have you shown that $0<1~?$
If so $n.

If not, what else can you use?

5. I'm not sure what you are implying here, I am fairly sure we can make the conclusion that 0 < 1, but what does that lead to?

6. Originally Posted by jstarks44444
I'm not sure what you are implying here, I am fairly sure we can make the conclusion that 0 < 1, but what does that lead to?
Add $n$ to both sides to get $n.
Now $n+1$ is an integer greater than $n$.