Stuntman I can't understand how it makes no sense to you, if someone asks you what the date is you would say 31st of may, 2013... 31/05/2013
I think I need to give a little more context to what I mean by date format. When I speak a date casually or in a sentence, I will say, "May 31st, 2013." This is generally how people say the date in conversation. If the year is obvious or implied, it is left out. If the month is also obvious or implied, it is also left out. For instance, if someone asks me when is the first day of summer, I would just say, "June 21st" or "the 21st." This convention is part of the English language (at least in Canada). I don't see people using proper English to start changing.
When I see it written in a way that is not used in a sentence, like in a form to be filled out, I like using the metric format which is YYYY-MM-DD with leading zeroes. The reason is that outside of any conversational context, I like seeing the most significant digits first. As I work in IT, this format makes it easier to sort by date. I find this format is easiest for me to recognise whatever part of the date that is important. If I know the year, I just look at the second and third part which has the month and day. If I know all of the dates are for the same month, I just need to look at the day. The metric format just makes sense for me when looking at numerical represenations of dates.
Continuing with the IT theme, if you need to include the time as well, you can append the time in HH:MM:SS using the 24-hour clock and leading zeroes. Again, it makes the time and date easy to sort and if you are focussing on only the minute or second, it corresponds with the convention of the most significant value on the left to the least significant value on the right.
When I see dates written in the dd/mmm/yy format or mm/dd/yy format, I just get confused. I find that I encounter date formats that are all over the place. Everyone seems to have a different preference or convention. My preference is the metric format of YYYY-MM-DD which I actually first learned in my typing class back in high school. It makes sense from a mathematical point of view and works for whenever I use dates. At my company, we actually have two formats one for IT related items and one for everything else.
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On another note, I find that the spoken language for time is also all over the place. When the time is 10 hours and 30 minutes, most people I know say, "ten thirty." Occasionally, I would hear people say, "half past ten." One time, someone from Ireland said, "half ten." I was thinking, "Half ten? That's five."

It wasn't until later that I realised he meant, "half past ten." :hmmmm: