Here's my proof that we will never prove the existence of true randomness.
* To demonstrate the randomness of the members of a set, we must examine the entire set.
* A candidate set cannot be finite in size, because a finite set is by definition not random.
* Therefore the only legitimate test of randomness is against an infinite set.
* To examine all the members of an infinite set would require infinite time.
This doesn't mean randomness doesn't exist, it only addresses the issue of proof.
