Finding a point in an infinite space

[JCarter426]

You are actually disproving the point you make in the second paragraph with what you plainly state in the last one. Since one only needs countable infinity of questions to obtain any irrational number exactly, then getting just any finite number of digits will require finite amount of questions.

Hrm, that depends on whether an answer with a finite amount of digits - a decimal approximation - is counted as a correct answer. Yes, I suppose if you accept a finite amount of digits as a valid response, then we're back in the realm of rational numbers, so of course you only need a finite amount of questions. But a decimal approximation isn't exactly the same number, is it? That's not the case for any irrational numbers, or even many rational ones in base 10. So the issue, I think, is that the person asking the question magically knows all the digits and is able to check them to decide whether our approximation should count... which is all certainly impossible. So my rephrasing of the question is still not a remotely realistic scenario, sorry.