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Did the year zero never exist ?
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Absolute value. Both systems count time from the same epoch, or zero point.
One year before the epoch is 1 January 1BCE One year after the epoch is 31 December, 1CE.
Half a year before the epoch (-0.5 years) is June 30, 1BCE. Half a year after the epoch (0.5 years) is July 1st, 1CE. These dates occur within the first year before the epoch, and the first year after the epoch, respectively.