>>20
hmm, I don't know, define what is a physical process, and maybe we can work something out. We'll basically need to restate the proposition, there exists a set with cardinality greater than set of the integers, but smaller than the set of real numbers, using terms that relate to something that you call a physical process. If we can find a representation for the real numbers in a "physical process" and a representation for the integers in a "physical process," then we can reformulate the original abstract question using a new vocabulary.
Let X be a something in a "physical process" that corresponds to the integers.
Let Y be something in a "physical process" that corresponds to the real numbers?
Is there a thing Z in a "physical process" that has more stuff in it than X, but less stuff in it than Y?
Now make a machine that simulates the question, and push the on button. There ya go.