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> This way I know that 14:00 today + one month is still 14:00 in my "internal" time format

Unless there's a leap second in that month. Then it would be 13:59. Maybe you don't care, but some people do. It could have legal or technical ramifications.

> Now, if I cannot really add a month anymore (and I cannot in TAI, because months don't even really exist in TAI, since TAI isn't a solar year).

What do you mean by month? Calendar months are obviously irregular (thanks February). "30 days" makes perfect sense in TAI. Indeed, 14:00 today + 30 days would always be 14:00 in TAI.



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