The 24 hour system: 23 -> 0 -> 1
How is that different than 11 -> 12 > 1 ?
Yes I get it that in normal integers, 1 is not after 12, but neither is 0 after 23.
How is that different than 11 -> 12 > 1 ?
Yes I get it that in normal integers, 1 is not after 12, but neither is 0 after 23.
The 24 hour system: 23 -> 0 -> 1
The 12 hour system: 11 PM -> 12 AM -> 1 AM
In the 24 hour system, there's a single point where the new day starts, and it's the transition from 23 to 0.
In the 12 hour system, where does the new day start? Numbers tell you it's 12 -> 1, but it's actually 11 -> 12. You have no way to figure the answer to OP's question out without additional context.
As others already pointed out in this thread, a 12 hour system using 0 instead of 12 would make it much more intuitive, although now you'd end up with either using 0:00 PM for noon, which feels strange, or using 0:00 AM and 12:00 PM, which is inconsistent. The 24 hour system has no such issues and has a massive advantage over creating new systems - people are already familiar with it.
I honestly am trying to understand the point being made. Isn't when the day starts obvious in either case? We know when the new _day_ starts because the date rolls over at that time. No one thinks the day starts at 12:00 in the 24-hour system, or 12:00pm / noon in the 12-hour system?
> ... there's a single point where the new day starts ...
Is this what you're saying: that in the 24 hour system, there's one point in time where the clock resets from a high number to zero, and that's also when the day starts. Therefore, it is "not confusing."
I felt rather that the problem the OP stated was simply "I am used to the 24 hour system and I was communicating with someone who was used to the 12 hour system. They naturally gave me a time of 12:00am but I didn't notice that am part and assumed they meant the same "12" that I understand as "12" in my system. So I missed an exam."
That's an additional reasoning you have to do in order to explain the non-intuitive fact that the new day starts when transitioning between hour 11 and 12. You can't come up with that conclusion based on clock system alone, you need to reach for the calendar. It makes you jump additional mental hoops, making it error prone (as evidenced by this thread).
> but I didn't notice that am part and assumed they meant the same "12" that I understand as "12" in my system
No, people who use 24 hour system are usually familiar with 12 hour system as well (guess what's there on analog clocks?). It's just this one special case of 12 AM/PM that's confusing, because you can make convincing arguments for having it both ways.
But since the midnight is the same distance from the noon, before (AM) or after (PM), in theory both should be reserved for midnights (the past one and the future one), and noon, too, should be both AM and PM - at 0 hours.
The only real solution for this mess is the one that everyone uses: just burn the meaning of 12:00 AM as midnight into your brain, and those who fail to do so are in for a trouble.
I do understand that having two different 12's in a day introduces an ambiguity about which one is the "real start" of the day just based on "12:00" alone.