Hilbert’s Hotel - An Ingenious Explanation of Infinity

What is ∞ - 1? And why?

Kasper Müller
Cantor’s Paradise
7 min readDec 30, 2021

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Hilbert’s hotel, Infinity, cardinality and bijections.
David Hilbert - picture from Wikimedia Commons

Imagine that you arrive at an infinite hotel, that is, a hotel with infinitely many rooms in it.

You need a room, the only problem for the receptionist (besides perhaps having a big guest book) is that the hotel is fully occupied and now he needs to find a room for you.

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Mathematician, programmer and writer interested in the mysteries of the Universe, fascinated by the human mind, music and things that I don’t understand.