I know how to prove real number is uncountable. But since both real number and natural number are linear ordered, it feels like there is some one to one relation between those two. Like the infinite hotel story, since they are both ordered, we can move them in the hotel one by one. But this is obviously wrong, I just can not figure out why. Thanks.
2026-04-24 22:48:28.1777070908
Why real number is linear ordered (total ordered) but uncountable?
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