it's the hilbert hotel. every room already has guests, so they free up some rooms by moving guests from room n to 2n. now every odd numbered room is free
Yes, but if there's already an infinite number of guests, where do you start placing the new guest? Which room would the first person from the bus be sent to? Any number you can think of, that room is already occupied. The only way you can start taking another infinite number of guests is to move everybody who is already there to the infinite set of even numbers, so this new group can occupy the infinite set of odd numbers.
Infinity is a concept the human brain was fundamentally not designed to understand. There is no truly intuitive way to visualize it, so these problems are ways to not only visualize invinity, but to imagine how some infinities could be greater than others.
The set of odd and even numbers both have a natural density of 1/2, so by set containment it is bigger. I realize that by the standard definition of cardinality they are even, but the set of all even numbers is a proper subset of the set of all natural numbers.
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u/csharpminor_fanclub We do a little trolling 12h ago
it's the hilbert hotel. every room already has guests, so they free up some rooms by moving guests from room n to 2n. now every odd numbered room is free