An integer p is prime if no positive integers other than 1 and p divide p.

You may assume that all integers greater than or equal to 2 may be written as a product of primes. (Proof is here:.ps, .pdf.)

So here's the problem: Prove that there are infinitely many prime numbers.

This is one of the classic examples of an indirect proof, wherein one proves a statement by assuming it is false and deriving a contradiction. You might wish to use this style of proof for some of the many problems we'll encounter involving linear independence.

If you want criticism from me, you can write up your proof in the space below and submit it; I'll return it with comments at the next section meeting. (You get absolutely no credit for doing this, but the feedback might prove beneficial.)