Finding a point in an infinite space

[Excession]

It does match. Computability means being able to calculate an arbitrary digit of the decimal expansion. We can do this for numbers like sqrt(2), pi, e, and other constructed transcendentals. There are numbers we can't do this for, and a lot of them involve elements of randomness.

Ah, thanks. I guess it's been I while since I studied this stuff properly.

You always have a next digit. 1.0 and 1.00 are equivalent, etc.

For the binary digit version on real numbers, you would have to ask if the digits repeated, then narrow down the length of the repeat, and "1.00000..." is just a trivial case of that.