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There is no last guest. There are infinitely many guests.

Thanks for chiming in.

I have trouble with that, though - if there's a "first guest", then I don't see there can't be a "last guest".. "room 1" and "room n" (as the article labels them) are equally arbitrary if there are infinitely many.

That’s the difference between all the integers (from negative infinity to positive infinity) vs just the natural numbers (from 0 to positive infinity). You can have infinitely many guests starting from a particular first guest.

Ah, cool! I can see that, thanks. :)

In that case I'd probably rephrase my original objection to say the "next guest" has nowhere to go, except when the they depend on the "next next" (etc.) guest finding a room in a "full" hotel - but I can see how that situation "never" comes up since they can pass the burden along infinitely.

I just feel like someday at the end of time, this poor unassuming new guest is gonna get cheated out of a room..

Yep, this is what makes Hilbert's hotel (and infinity in general) counterintuitive. When we try to apply reasoning that's correct for finite sets to infinite sets, very often it becomes incorrect.

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