Proof of the infinitude of composites.

Assume there are a finite number of composites, say n.
Then let the set of composites be (c₁, c₂, ... , c_n)
If we take the product (c₁ x c₂ x ... x c_n, then clearly this is a composite number since the product of composite numbers is composite.
So long as n > 1, then c₁ x c₂ x ... x c_n is not in the list (c₁, c₂, ... , c_n)
Proving n > 1 is left as an exercise to the reader.

π