This algorithm seems to be consistent with counting the real interval, what's wrong with it? So I've been imagining infinite sets, specifically the real numbers,
Here's the algorithm,
start at .1, then as follows, .2, ... .9, .01, .11 ... .99, .001, ... .999, etc.
Why wouldn't this generate the reals at infinity? I realize this is a countable set, it's informally an inversion of 1 ... infinity, so it's countable. Yet if you describe .1 as existing in column 1 and .99 as column 99, that would imply that if you choose a .2516 at column 1 not equal to .1, that it would show roughly in column 6152.
Where am I mistaken?

What you have described is a van der Corput sequence, which does get arbitrarily close to each real number in the interval, but the sequence doesn't contain numbers like $\frac19$ that don't eventually terminate. Every number in the sequence has a terminating decimal expansion.
