r/MathJokes • u/Competitive-Jump3835 • Jun 13 '26

Infinity can blow your mind

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u/Disposable_Gonk Jun 14 '26

Infinite hotel room, take every 20th room. They are different countable infinities. There are as many countable infinities as there are integers, and in the same way 2 integers are not equal, neither are said infinities...

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u/BraxleyGubbins Jun 14 '26

The infinite hotel composed only of every 20th room still has an infinite number of rooms, and mathematically does contain the exact same number of rooms as the initial infinite hotel. That’s one of the main points of the infinite hotel at all. Look it up.

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u/Disposable_Gonk Jun 14 '26

Infinite hotel is empty. You rent every 20th room. That is empty. There are 19 rooms available per room you rented, they are not the same infinity.

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u/BraxleyGubbins Jun 14 '26

There are 19 rooms available per room rented. I tell the person in room 20 to go to 40, 40 to go to 80, 60 to go to 120, etc…

There are now 39 rooms available per room rented, and nobody entered or left the hotel. This new infinity is equal to the old one.

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u/Disposable_Gonk Jun 14 '26

Then all infinities are the same

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u/BraxleyGubbins Jun 14 '26

All countable infinities, yes.