How can some infinities be bigger than others?

Re:How can some infinities be bigger than others? by firstlink on Thursday April 20, 2023 @02:42PM (#35644347)

> If you pick one and call it N, there's an infinite quantity of real numbers between 0 and N and between N and 1. Therefore it's impossible to assign an index to N.

This isn't "sloppy language", it's just wrong. Don't try to downplay spreading misinformation. It remains true that there are infinitely many rationals in (0, N) and (N, 1), and yet it is entirely possible to enumerate the rationals (i.e. assign indices).

> There's an infinite number of those between 0 and 1 as well, but because it's a subset, there are "fewer" of them.

Also misinformation. (0, 0.5) is a subset of (0, 1) yet the two sets have the same cardinality, whether we take them both in Q or both in R.

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Re:How can some infinities be bigger than others? by roarcher on Thursday April 20, 2023 @03:11PM (#35644758)

> This isn't "sloppy language", it's just wrong.

Yes, no less than four people have explained what's wrong with my comment. I made the "sloppy language" edit before I fully understood them.

> Don't try to downplay spreading misinformation.

> Also misinformation.

LMAO. Every incorrect thing you see on the internet isn't the work of a Russian troll or whatever you're trying to accuse me of here. Have you considered getting a life?

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