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.
Year zero
Dionysius did not use AD years to date any historical event. This began with the English cleric Bede (c. 672–735), who used AD years in his "Historia ecclesiastica gentis Anglorum" (731), popularizing the era. Bede also used a term similar to the English before Christ once, but that practice did not catch on until very much later. Bede did not sequentially number days of the month, weeks of the year, or months of the year. However, he did number many of the days of the week using a counting origin of one in Ecclesiastical Latin. Previous Christian histories used "anno mundi" ("in the year of the world") beginning on the first day of creation, or "anno Adami" ("in the year of Adam") beginning at the creation of Adam five days later (the sixth day of creation according to the Genesis creation narrative), used by Africanus, or "anno Abrahami" ("in the year of Abraham") beginning 3,412 years after Creation according to the Septuagint, used by Eusebius of Caesarea, all of which assigned "one" to the year beginning at Creation, or the creation of Adam, or the birth of Abraham, respectively. Bede continued this earlier tradition relative to the AD era.