Hilbert’s Hotel: You’re Missing the Best Bit! | Math - Medium

Infinity, enumerating the rationals and elegant solutions to innocuous problems by Ollie Watkinson, Writing on Mathematics and Philosophy, published in published in Cantor’s Paradise.

Photo: Maxime Lebrun on Unsplash“The infinite! No other question has ever moved so profoundly the spirit of man.” — David Hilbert.

Hilbert’s hotel paradox is a beautiful demonstration of the countably infinite. A coach full of the natural numbers, stretching backwards forever, arrives at a hotel with endless rooms and a maths-wizz receptionist. After allocating every guest a room the receptionist returns to her desk only to find another set has arrived! A brief negotiation almost always allows the receptionist to rearrange the current guests, leaving room for the newest. The details of these theoretical negotiations can be both ingenious and infuriating. In building his hotel in 1924 David Hilbert created a brilliant framework for discussing the mathematics and philosophy of infinity.

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