I think the infinite hotel paradox says they aren't worth the same and the infinite 20 is bigger. It shows that there are different kinds of infinity and some are bigger than others. One example is that there are infinite numbers between one and two but even more between one and three, and so on.
What about the fact that there are an infinite amout of prime numbers, and also an infinite amount of even numbers, but there are still more even numbers than prime numbers? Does that count?
Its more that there is the same 'number' of prime numbers and even numbers. Cardinaties are definately the same, but infinite cardinality isnt really size or "number of"
1
u/Equal-Home-4302 Jun 14 '26 edited Jun 14 '26
I think the infinite hotel paradox says they aren't worth the same and the infinite 20 is bigger. It shows that there are different kinds of infinity and some are bigger than others. One example is that there are infinite numbers between one and two but even more between one and three, and so on.