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Huh, but there is no 1 second gap between 23:59:59 and 00:00:00. The time is 23:59:59 for a whole second, and then once that second is done, the time is 00:00:00 the next day.

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It depends whether you interpret "23:59:59" as being an instant (1 second before the end of most days) or a duration (the last second of most days).

23:59:59.500 is after 23:59:59 when interpreted as an instant, but it is part of 23:59:59 as a duration.

Thats why the day doesn't end at the instant of 23:59:59, nor does it end at 23:59:60 (if there is a leap second). It actually ends at 24:00:00. Which is the same instant in time as 00:00:00 of the following day. Every conforming implementation of ISO 8601 should know about that. And all software should conform to ISO 8601.

That's how I would interpret it as well. It gets easier to imagine when we put in milliseconds. Why would 23:59:59.456 already be the following day?

And then there are leap seconds.

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