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The proleptic Gregorian calendar is produced by extending the Gregorian Calendar to dates preceding its official introduction in 1582.
Bede and later historians decided not to use the Latin zero, nulla, as a year, so the year preceding AD 1 is 1 BC. In this system the year 1 BC is a leap year (likewise in the proleptic Julian calendar).
Mathematically, it is more convenient to include a year zero and represent earlier years as negative. This is the convention used in the "astronomical Gregorian calendar". In this system the year 0 is a leap year.
Note that because the Julian calendar was in actual use between 4 and 1582, historians and astronomers prefer to use it. Likewise, the proleptic Julian calendar is used to specify dates before AD 4, its first quadrennial leap year (leap years between 45 BC and AD 4 were irregular). But when seasonal dates are important, the proleptic Gregorian calendar is sometimes used, especially when discussing cultures that did not use the Julian calendar.
fr:Calendrier grégorien proleptique
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