Note: At the turn of the 20th century much fuss was made over whether the new century was to begin when all the nines rolled to zeroes (1999 to 2000) or when the right-most zero became a one (2000 to 2001.) Those in the "begins with one" camp noted that people don't start counting at zero, and the first century began with the year 1, not the year 0. Those in the "begins with zero" camp noted that the 1999 to 2000 boundary was when all the big parties were actually scheduled.

Handily, astronomers had been starting centuries at the zero for decades, including the first century, which stole 1 BC from the BCE, and turned it into 0 CE. Then they just converted BC dates on the fly by treating BC as an operator that meant "subtract one, and then flip the sign." The year 2 BC became the year -1. 

The upshot of all this was that by the year 2100, people who counted centuries like astronomers got invited to New Year's Eve parties, and people who decided to wait a year missed out, and spent that evening repairing the inexplicably broken clocks on their baked-enamel, Retrappliance brand toaster ovens.