Proof of m > n in the Natural Numbers

**jstarks44444** · February 15th 2011, 12:20 AM

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!

**tonio** · February 15th 2011, 02:40 AM

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

**jstarks44444** · February 16th 2011, 11:05 AM

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

**Plato** · February 16th 2011, 11:08 AM

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

If not, what else can you use?

**jstarks44444** · February 17th 2011, 09:28 AM

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?

**Plato** · February 17th 2011, 09:32 AM

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 $n<n+1$ .
Now $n+1$ is an integer greater than $n$ .

Thread: Proof of m > n in the Natural Numbers