Ask your math prof. Your philosophy prof. is a moron who doesn't understand the concept of infinity.

To make this concept clearer, put it in physical terms. Take the Earth's atmosphere, which is composed of 78% nitrogen, 21% Oxygen, 1% Argon. Now if you go anywhere in the atmosphere and sample one molecule, you have a 78% percent chance of it being nitrogen, 1% of it being Argon. If you double the size of the atmosphere, same thing. Expand Earth's atmosphere to fill the entire universe, the ratios don't change. If you make the universe infinite, go to any spot and sample a molecule, the ratios still don't change, Argon is always far less likely to be picked.

In the prime number example, the incidence of prime numbers actually decreases as the size of number set increases. So the chance of picking a prime number goes to 0 as N goes to infinity. Note that it never actually reaches 0. The chance of picking an odd number stays the same at 0.5 no matter how large N gets.

You can tell your professor he's a [censored] monkey.

edit: Looking at this I find it hard to believe anyone can be so retarded. I'm guessing this was a homework question and I just did it for you [img]/images/graemlins/smile.gif[/img]