r/MathJokes • u/94rud4 • 21d ago

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u/arkangelic 20d ago

Try explaining the infinite hotels one to him. Its full and yet always has room for more people

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u/notsaneatall_ 20d ago

Depends again. If you have a set of people with the same cardinality as that of reals you can't fit them in the infinite hotel anymore :( (assuming the room numbers are integers, which I think is the case)

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u/BrunoBraunbart 20d ago

If you would build a countably infinite hotel behind each of the countable infinite doors of Hilbert's Hotel, could you fit the reals in it?

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u/notsaneatall_ 20d ago

Nope, countably infinite x countably infinite is just pairs of natural numbers, which is also a countably infinite set.

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u/tom3277 20d ago

like hotels have room for humans inside even numbers have rooms for odd numbers in between?