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Year zero does not exist in the Anno Domini system usually used to number years in the Gregorian calendar and in its predecessor, the Julian calendar. In this system, the year 1 BC is followed by AD 1 . However, there is a year zero in astronomical year numbering (where it coincides with the Julian year 1 BC ) and in ISO 8601:2004 (where it coincides with the Gregorian year 1 BC ) as well as in all Buddhist and Hindu calendars.
The year 0 is that in which one supposes that Jesus Christ was born, which several chronologists mark 1 before the birth of Jesus Christ and which we marked 0, so that the sum of the years before and after Jesus Christ gives the interval which is between these years, and where numbers divisible by 4 mark the leap years as so many before or after Jesus Christ.
Originally, years were adjectives (1st year, second year, et cetera). This system is because, at the time, people did not know about 0. Cassini, being a mathematician, wanted 0. He may or may not have wanted 0-Time (a singularity of time), but he wanted to maintain the cycle of leap years. He defined the Year 0 as the year-long duration containing the leap year before the Year +4. Because the system is based on durations of time instead of a temporal singularity of 0-Time, the 0th year is unsigned. The years work thus: