Using "12 A.M." and "12 P.M." is actually WRONG! (Common Error in English)

The time should be stated as 12 noon and 12 midnight. The letters “a.m.” stand for ante meridiem, a Latin phrase which means “before noon” and the letters “p.m” stand for post meridiem, which means “after noon”.
To say 12.00a.m or 12.00p.m at noon would therefore be wrong, since noon cannot be before or after itself. As for midnight, is it before or after noon? It would be safer and clearer to call it 12:00 midnight.