How can some infinities be bigger than others?

Re:How can some infinities be bigger than others? by cubefox on Wednesday April 19, 2023 @09:05PM (#35635190)

> Both of these are incorrect you can create a 1-1 mapping between all of these sets so they are the same "size".

They are incorrect if you define "the same size" as the existence of a one-to-one mapping. But if you think that a proper subset is never the same size as the original set, then you won't accept that definition.

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Re:How can some infinities be bigger than others? by rtkwe on Thursday April 20, 2023 @08:57AM (#35639232)

That's only useful in comparing subsets though and we need a way to compare the size of any possible pair or group of infinite sets, given that the bijection method makes way more sense. Even though it's slightly unintuitive to laymen how can one thing be larger than another if for every member of one group I can match them with a member of the other group, provably for all the infinite members of either group?

I get there's a conflict with intuition there but infinities an inherently unintuitive.

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Re:How can some infinities be bigger than others? by cubefox on Friday April 21, 2023 @01:23PM (#35657093)

It's more an argument not to assume there are infinities of different sizes. That would also get rid of most mathematical paradoxes related to infinity.

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