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A comment on How can some infinities be bigger than others?. Parent comment

Re:How can some infinities be bigger than others? by Skeime on Thursday April 20, 2023 @04:57AM (#35637749)
Because continuity is not required here. There are non-continuous bijections between R and R^2.
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Re:How can some infinities be bigger than others? by yarg on Thursday April 20, 2023 @05:12AM (#35637822)
How is continuity not required?

If there are holes in the map does it really cover the whole space?

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Re:How can some infinities be bigger than others? by Skeime on Thursday April 20, 2023 @01:06PM (#35642997)
I think you have misconceptions about what continuity means and I’m not even sure what you mean with holes.

As a simpler example: The map that multiplies each rational number by -1 and keeps irrational numbers as they are is bijective (it’s its own inverse), however it is nowhere continuous.

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