It's simple mathematics to prove otherwise.

Take, for example years.

We are in the 21st Century, yet the year is 2010. That doesn't make sense, unless you count century zero. Century (c) is worked in the nth. C = C-1.

So century zero would be the first century. (The first being zero)

Apply that to time, Minutes (m) is worked in the same degree. M = M-1. The first minute of the day, is minute zero. Which on a 24h clock is 00:00, or in AM and PM, is AM. The first minute of the day, ergo, morning.