Have you read...

your Numerical Recipes in * today?

>>4
Let's assume there such a largest number n.
Peano's axioms state that n has a successor (which we can call n' or n+1 in simpler terms) which is how we define a greater number. Contradiction.
There is no greatest number in N, but there is the smallest number 0.
If you try to define the set as finite, you'll end up with the same trivial contradiction which shows that there will always be more elements.
I'm guessing you reject any kind of inductive reasoning as well, and you don't accept any abstract concepts unless they are present in this one specific mathematical object we call our universe.

>>7
Ad-hominem's are not a valid reasoning technique.
You're claiming there are such things as "natural numbers", right? Otherwise we wouldn't be having this discussion in the first place. You're going to need a set of axioms to define them. Peano's axioms (or even only 2 simple one-line statements) are enough to show that the set of natural numbers is infinite, in the sense that there's no greatest number. If you don't like Peano's axioms, there are many other axioms which can be shown to be isomorphic to Peano's and which also define the set just as well. You'll end up with the same conclusion regardless.