Finding a point in an infinite space

[crayzz]

I think we just proved uncomputable numbers don't exist in this hypothetical scenario, because there always exists a series of yes or no questions that we can ask our magic all-knowing questioner to compute any number to any degree of precision.

Which is another way of saying this scenario could never exist.

Which, I mean: that's obvious, but it's kinda neat stumbling over an actual proof for it.

I don't agree, because even an arbitrarily precise approximation isn't the actual number. Getting the exact irrational number would require infinite time, which I think doesn't match the definition of "computable".

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.