[aantthony]

Ah, yes. The definition I tried to use was from Wikipedia, in full: "In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers." I missed the part where it said finite. Thank you for correcting that.

If you take your sequence construction, then by removing duplicates from the sequence, this new sequence would allow finding a "next" element.