Frequently Asked Questions
What is Hilbert's hotel?
A thought experiment about a hotel with infinitely many rooms, all occupied. Even so, more guests can always be accommodated via clever reassignment.
How can a full hotel take new guests?
Move every current guest from room n to room n plus one. Room one is freed up. The hotel was full only in the sense that every room had a guest; with infinite rooms, you can always shift.
What about infinitely many buses?
Use a pairing function (such as bus i, seat j to room two to the i times three to the j) to assign every newcomer a unique room. Infinitely many guests still fit.
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