It recently occurred to me that I've never seen a scheme to partition the real line into an uncountable number of half-open intervals. Is this possible?
Thanks.
2026-03-29 21:37:42.1774820262
Partition the real line into an uncountable number of half-open intervals?
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I suppose that you mean distinct half-open intervals; otherwise, the problem is trivial. It is not possible; any such interval will have a rational number, and there are only countably many rational numbers.