There are 24 hours in a day. Everyone knows that. And, if you buy a watch that indicates 24 hours, the numbers 1 through 24 appear on it as well. Obviously. Oh, what have we here? In the place of the 24, this English watch has a zero! But isn’t the 24 supposed to be there, instead?
What a fiddly affair. In legal terms, 0:00 and 24:00 are the same time instant. The difference in meaning is solely a question of different linguistic usage describing the same time instant. The expression of time as 0:00 describes a beginning; 24:00 describes an end. Therefore, the day begins at 0:00 but ends at 24:00. However, a watch, though it does show 0:03 a.m., will never show 24:03 p.m. In this regard, it is perfectly right to replace the 24 on the watch with a zero, although it does seem a bit unusual.
Whoever finds it all too complicated with 0:00 and 24:00, can simply say “midnight”. This way, he is always absolutely right.
Pocket Watch with 24-hour display, Frodsham, London, 1862, Inv. 2015-061