Representing Uncountable Sets
Andrej had a nice post on representing uncountable sets.
I think he goes off the deep end a little bit (in an entertaining way) at the end:
Even if we disregard the theoretical issues about computable vs. non-computable enumerations, we are still left with the question whether real computers “contain” non-computable sequences. Do they? Does the universe? Or do you claim that all streams of 0’s and 1’s that physicists are able to feed into computers are definitely computable? Perhaps physicists should devise an experiment that would tell us something about existence of non-computable streams. I think we would quickly discover that such an experiment is in principle impossible because we may only ever observe finite prefixes of a binary stream. According to the Verification principle this makes the question meaningless and any position about its truth an article of faith.