Astronomical year numbering
Cassini gave the following reasons for using a year 0:
Fred Espanak of NASA lists 50 phases of the moon within year 0, showing that it is a full year, not an instant in time. Jean Meeus gives the following explanation:
Although he used the usual French terms "avant J.-C." (before Jesus Christ) and "après J.-C." (after Jesus Christ) to label years elsewhere in his book, the Byzantine historian Venance Grumel used negative years (identified by a minus sign, −) to label BC years and unsigned positive years to label AD years in a table. He did so possibly to save space and put no year 0 between them.
Missing years (Jewish calendar)
Today, Hebrew dating places the creation of the world near the end of "Year One" AM and afterwards the first year of Adam's life as "Year Two" AM. However, Seder Olam Rabba shows that the Hebrew dating originally counted the first year of Adam's life as "Year Zero" AM. This may mean that the Hebrew dating has shifted in the course of history such that traditional dating of ancient events appears two years earlier than the modern Hebrew dating would be.