Finding a point in an infinite space

[Caerulea]

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