Named for David Hilbert (1862-1943), Hilbert presented his paradox (also known as Hilbert's hotel paradox) as an explanation of infinity and an extension of Cantor's continuum hypothesis. In revealing his paradox, Hilbert posited a hotel with infinitely many rooms, of which a finite number n are full. If a finite number x of new guests show up at the hotel and request rooms, all the newcomers can be accommodated if each of the n guests are moved x rooms down the hall. Since the hotel has infinitely many rooms, all newcomers are welcome, and this adjustment holds true even if all rooms at the inn are full. Hilbert's paradox, however, broadens this idea to a hotel with infinitely many rooms, all of which are full. If a new group of guests (of which there are infinitely many) arrive, it would seem that they could not be...