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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.

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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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