Finding a point in an infinite space

[Excession]

Warty Goblin's method also "bisects" the space of possible answers, in the sense that after each question the possible number of solutions is halved. (His method was asking if successive digits in the binary representation of each number are 0 or 1.) I don't believe it works for continuous spaces though. (Maybe one could add a step checking whether the number was less than a particular power of two, and then go to successively more precise digits?)

—Caerulea

For continuous spaces you can still reduce to a single number with a space-filling curve, then use a binary search between two whole numbers, but you will need an infinite number of questions to find an irrational number than way.

Edit: finding a rational number is actually the same problem, you're just looking for (x/y) rather than (x, y).

"Has the number ever been seen by a human before?" If yes the questions are now finite. If no begin infinite questions.

If you know the number is finite, and that is implied by it being a number, you don't need infinite questions. If nothing else you can just ask "is it 0?", "is it 1?" and so on. Number of questions equal to the number, so still finite.