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>days as durations rather than points

Isn't thinking of day X as the range [midnight of X, X+1 midnight) isomoprhic to associating it with a point for X, at least for purposes of considering coverage (e.g. both approaches work to show that there are 7 days that cover a week).



Yes, see the end of my comment:

> I think TheJosh mixed things up when trying to explain it (durations vs inclusive/exclusive)




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