I know what the paradox is, but how does it relate to our universe?
In: Mathematics
Hilbert’s hotel isn’t really a statement about our universe per say. It’s just a made up word problem to illustrate a property about infinity. Kinda like teaching division by using a made up problem about sharing a plate of cookies equally among a group of people.
Would you say that the cookie example tells us something about the universe? Not really, they just help you visualize a circumstance in which you might care about division.
In a similar way, Hilbert’s hotel is a circumstance where we might care about adding two infinite things together. It’s just that infinity behaves in weird ways, so the solution to Hilbert’s hotel seems like a made up solution to a made up problem. Infinity plus itself equals… itself. Exactly the same as itself. “Real” objects don’t typically work that way, so we have to make up this hypothetical story to make it digestible for laymen.
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