[andrewla]

I agree that the downvoting is unfortunate. I guess the assumption is that the post is simply a troll, which seems to be backed up by some of the down-thread replies. Even so, the original post just seems like a list of common misunderstandings about Cantor's notion of infinity and how it corresponds to the way that we use the word in colloquial use.

In defense of the GP, I think they were simply thinking of numbers in [0,1). If you write them backwards, it almost seems like it would work:

    1    ->  .1
    2    ->  .2
    ...
    9    ->  .9
    10   ->  .01
    11   ->  .11
    12   ->  .21
    ...
    3124 ->  .4213
    ...

Done!

Unfortunately, you are either stuck with the fact that some numbers (even simple rational ones) do not have a finite decimal expansion. In most formal proofs of the diagonal theorem, we use the infinite representation without trailing 0s (using trailing 9's instead) to force uniqueness, which makes it even trickier.

Or you're stuck trying to assume that there are natural numbers with an infinite representation, so the decimal representation of the rational number 1/3 would correspond to an actual natural number.