Assume there are a finite number of composites, say n.
Then let the set of composites be (c1, c2, ... , cn)
If we take the product (c1 x c2 x ... x cn, 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 cn is not in the list (c1, c2, ... , cn)
Proving n > 1 is left as an exercise to the reader.