This isn't right. Midday / midnight are not the 60 seconds it takes for a digital clock to go from showing 12:00 to 12:01. They are the infinitesimally small point in time that mark the transition between "before" and "after".

Like throwing a ball up into air, there is no time where it is not either rising or falling, but there is a point where it transitions from one to the other.

So midday is 12:00pm. As soon as the moment has been observed it has passed, and you are now "post meridiem".