Finding a point in an infinite space

[JCarter426]

Hmm...the point about countable infinities vs uncountable is I think the stumbling block that was making it difficult for me to wrap my head around, but different degrees of infinite makes it a bit easier. Would an uncountably infinite number of questions be insufficient to determine the point if it was "numbers" instead of "whole numbers", since that opens up fractions and irrationals and makes the problem also an uncountable infinite, or is the uncountable infinite of the problem still not so large that the uncountable infinite of the solution couldn't solve?

I don't know if you can have an uncountably infinite number of questions. It seems like the set would inherently be countable because you can say this is the first question, this is the second question, etc... and thus count them. Of course if you need any sort of infinity to answer the question, you're going to have problems answering it in the real world.

If you wanted to generalize the question for all numbers and be able to answer it realistically - i.e. without any sort of infinity - then I think you'd have to rephrase the question. Say, you aren't given an infinite amount of questions, but you also don't have to give all the digits, just enough for whatever degree of precision is specified. Like how we don't know all the digits of π but we can calculate it to whatever precision is required, given enough time.

So the problem instead is to determine x and y to n decimal places, given a finite amount of questions (however many you want, but not infinite). Can that be done for all numbers?

In that case, the answer is most certainly no, you can't do this for all numbers. You could do it for approximately 0% of numbers in existence. That's basically the definition of computable numbers, so of course it wouldn't work for uncomputable numbers, and most numbers are uncomputable.

If the potential number of questions is infinite as well most if not all of those issues should be negated in theory, shouldn't they?

EDIT:
Now that I think of it, maybe not. If the space is continuous then the number of points is uncountably infinite whereas the number of questions must be countably infinite. It should work in an infinite grid of integer coordinates though

The set of irrationals is uncountably infinite, but the amount of digits in an irrational number is countably infinite. So you can still brute force the problem by asking questions until each digit is known with only a countable amount of questions.