Let a hotel have a denumerable set of rooms numbered 1, 2, 3, .... Then any finite number n of guests can be accommodated without evicting the current guests by moving the current guests from room i to room i + n. Furthermore, a denumerable number of guests can be similarly accommodated by moving the existing guests from i to 2i, freeing up the denumerable number of rooms 2i - 1.

cardinal number | denumerable set