Hilbert's Paradox of the Grand Hotel
Version 1.0.0 · Updated 2026-07-30
CORE DEFINITION
A hotel with an infinite number of rooms, all occupied, can still accommodate a new guest (by moving guest in room 1 to room 2, room 2 to room 3, ... room n to room n+1, freeing room 1). Even an infinite number of new guests can be accommodated (by moving guest in room n to room 2n, freeing all odd-numbered rooms).
SCAFFOLDING EFFECT
Reduce cognitive load
Scheduling logic for infinite resources. In cloud thinking and digital asset management, resources (such as storage space, computing power) are theoretically 'infinite'. But infinite does not mean no scheduling is needed. This paradox reminds us that even with infinite resources, we still need to manage and allocate them effectively.
Anchor fast decisions
Hilbert's paradox of the Grand Hotel: A hotel with infinitely many rooms, all full, can still accommodate new guests by shifting each guest from room n to room n+1, freeing room 1 for a new guest; even countably infinite new guests can be accommodated by shifting each guest from room n to room 2n, freeing all odd-numbered rooms. This demonstrates the counterintuitive nature of infinite sets.
MINIMUM ACTION
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Source support: Explicit
- zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E5%B8%8C%E5%B0%94%E4%BC%AF%E7%89%B9%E6%97%85%E9%A6%86%E6%82%96%E8%AE%BAverified
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