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As the sun rises in the sky in the morning it approaches the meridian. The meridian is the imaginary line from the north pole to the south pole going through the highest point in the sky. In the morning, the sun is before the meridian (Ante Meridiem in Latin), and in the afternoon is after the meridian. (Post Meridiem in Latin.) Thus, morning hours are suffixed by A.M. and afternoon hours by P.M.
The correct designation for noon, therefore, is 12:00M.
Midnight would be either 12:00 A.M. or 12:00 P.M., depending on which way you are facing. Of course with a 24 hour clock there is no confusion.
An old related joke about imaginary lines--
When the young schoolboy was asked to define the equator, he replied that it was a menagerie lion running around the center of the earth.