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Maybe someone can help me understand, not a mathematician or engineer. It seems like the hotel is “full” but because there are infinite rooms, when new guests a
by catillac 5y ago
Maybe someone can help me understand, not a mathematician or engineer. It seems like the hotel is “full” but because there are infinite rooms, when new guests arrive they just move everyone to their room + 1 and make space at room 0.
I don’t think I understand the significance here, since it seems logical.
- simonh 5y agoIt is logical, and that's the point. It's simply explaining various properties of infinite sets and techniques for doing operations on them that are provably correct.
- jedimastert 5y agoThat point being made here is that infinity changes some pretty basic assumptions about how we think of things like "full" and "counting".
- lupire 5y agoIt's incompatible with physical reality, no such hotel could exist. The paradox is in applying infinite math to physically realistic problems.
- joppy 5y agoThere are two ways you can define the hotel as being full: 1) The hotel is “full” if all the rooms are occupied. 2) The hotel is “full” if there is no way to rearrange the existing guests to leave an empty room. These two definitions of “full” are equivalent for finite hotels. The ‘paradox’ is illustrating that these two definitions are not the same for infinite hotels. It serves as a useful reminder that there might be more “space” in infinite sets than we are used to in the finite case, and that if we are dealing with infinite sets we should keep in mind the fact that (1) and (2) (or whatever analogues are relevant for our problem) might be different, despite seeming the same based on our real-world experience.
- catillac 5y agoThis is really helpful, thank you for the thorough explanation