Mind Matters Natural and Artificial Intelligence News and Analysis

# TagHilbert's Hotel

## Math Fun: Hilbert’s Hotel Manager Copes With Infinity With Poise!

What, exactly, happens when a would-be guest shows up at a fully booked hotel — with infinite rooms?

Hilbert’s Hotel is a thought experiment that the great mathematician David Hilbert (1862–1943) developed to help us see the “counterintuitiveness of infinity.” He asks us to imagine a hotel which is “full” — except that because it is infinite, it can always create one more room. Mathematician Marianne Freiberger explains: Suppose that your hotel has infinitely many rooms, numbered 1, 2, 3, etc. All rooms are occupied, when a new guest arrives and asks to be put up. What do you do? It’s easy. Ask the guest in room 1 to move to room 2, the guest in room 2 to move into room 3, the guest in room 3 to move into room 4, and so on. If there Read More ›

## Why Just Anything Can’t Happen via Infinite Universes

We can see why not, using simple mathematical reasoning in this universe

Can anything happen if there are an infinite number of universes each with an infinite number of possibilities in each? Can you be bald in one universe and fully haired in another? Can you have two eyeballs in this universe and three in another? The answer is no. In a nutshell, the reason is that some infinities are bigger than other infinities. (And this is not a claim like infinity plus one is bigger than infinity. Infinity plus one is still infinity.) The number of points on a line segment from, say zero to one, is a bigger infinity than the number of counting numbers {1,2,3,…}. We can label the infinite number of universes in the multiverse as universe #1, Read More ›