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
All eras used with Hindu and Buddhist calendars, such as the Saka era or the Kali Yuga, begin with the year 0. All these calendars use elapsed, expired, or complete years, in contrast with most other calendars which use current years. A complete year had not yet elapsed for any date in the initial year of the epoch, thus the number 1 cannot be used. Instead, during the first year the indication of 0 years (elapsed) is given in order to show that the epoch is less than 1 year old. This is similar to the Western method of stating a person's age – people do not reach age one until one year has elapsed since birth (but their age during the year beginning at birth is specified in months or fractional years, not as age zero). However, if ages were specified in years and months, such a person would be said to be, for example, 0 years and 6 months or 0.5 years old. This is analogous to the way time is shown on a 24-hour clock: during the first hour of a day, the time elapsed is 0 hours, "n" minutes.