There are different “kinds” of infinity. For example, there is an infinite amount of natural numbers, and there is an infinite amount of real numbers. Still, natural numbers only make up a tiny part of real numbers, so while both are infinite, the set of real numbers is bigger. Hilbert’s Hotel is an analogy meant to convey how to deal with these different notions of infinity.
Not really. The guests move to a room with double the number, freeing up an infinite number of rooms.
So the change is from natural numbers to even numbers, freeing up odd numbers. Those infinities are the same, but you can still do this because infinities are weird.
There are different “kinds” of infinity. For example, there is an infinite amount of natural numbers, and there is an infinite amount of real numbers. Still, natural numbers only make up a tiny part of real numbers, so while both are infinite, the set of real numbers is bigger. Hilbert’s Hotel is an analogy meant to convey how to deal with these different notions of infinity.
Not really. The guests move to a room with double the number, freeing up an infinite number of rooms.
So the change is from natural numbers to even numbers, freeing up odd numbers. Those infinities are the same, but you can still do this because infinities are weird.