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It's technically correct, since am=ante meridiem="before noon". And midnight, of course, comes before noon. You can call it 0am, but then you'd have to call noon 0pm which is weird. Plus, remember most analog watches in the world have a big "12" on top.

The obvious fix would be switching to 24hr.

There's no reason you have to kill the 12. It would work to just have 1:00 be the first hour of the day, have the day be 1:00-12:59am followed by the same as pm. 1:00pm is "meridiem". No change to analog watches.

Obviously there's zero chance of switching to that at this point from a pragmatic point of view but it does just work out fine.

Given an AM/PM 12 hour system, unless it's obvious from context, the best thing is usually to write noon or midnight. 12am and 12pm in isolation can absolutely be confused. Even if I know the convention, I don't know if the person writing 12am does.

What does am mean?

It’s currently 1300, an hour ago was 1200, two hours was 1100

Yeah but it’s 2021/09/14 21:10 where I am, perfectly big endian for me