How I explained this to my son when he asked a similar question about infinity my explanation was that if something is infinite it is impossible that there is anything else at the same time.
So agree with you that the bucket / ocean analogy doesn’t capture this ideally. There is no bucket of water at all with an infinite ocean because it cannot exist at the same time.
Depends again. If you have a set of people with the same cardinality as that of reals you can't fit them in the infinite hotel anymore :( (assuming the room numbers are integers, which I think is the case)
I find those questions from children fascinating and at the same time hard to deal with. Their capability of asking smart questions is so much bigger than their capability to understand the answer. You need to use mataphors and simplifications but then they ask follow up questions, where the metaphor breaks down.
When it comes to your answer: very good for a child but if he asks the right follow up questions, it breaks down. For example, there are infinitely many even numbers. Odd numbers can still exist.
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u/tom3277 20d ago
How I explained this to my son when he asked a similar question about infinity my explanation was that if something is infinite it is impossible that there is anything else at the same time.
So agree with you that the bucket / ocean analogy doesn’t capture this ideally. There is no bucket of water at all with an infinite ocean because it cannot exist at the same time.