No year zero exists, or can exist, mathematically speaking.
The best way to conceive of this is through the use of a number line.
A dot in the center, a first ray extending from the center dot to the right, and a second ray extending from the center dot to the left.
Hash marks are not labeled with numerals but instead merely indicate the transition between years.
Braces labeled with numerals indicate the span of a year, a decade, a century, a millennium, etc. A year is represented in this way as a certain standard distance along the number line.
The first “braced” span between the center dot and the nearest hashmark, one to the left of the center dot, and the other to the right of the center dot, is labeled with the numeral “1”.
The last year in the first millennium was year 1000. The first year in the second millennium was year 1001.
Similarly, the last year in the second millennium was year 2000. The first year in the second millennium was year 2001.
The last year of the twentieth century, for example, was the year 2000. Then, the new year’s eve ball dropped and we found ourselves, on January 1, 2001, in the twenty-first century.
The New York Times celebrated the arrival of the twentieth century in the paper it published on January 1, 1901. Nobody argued at the time with the mathematics the New York Times used to support its editorial decision to commemorate the arrival of the twentieth century.
The New York Times strangely allowed January 1, 2001 to arrive with no such fanfare within the pages of its newspaper, despite the arrival of not only a new century, but a new millennium. Why do you think this was?
Don’t bother. This Guy will answer:
Metastasizing societal ignorance and stupidity.
There is not and never was any such thing as a year zero.
I agree in general that year zero is a bad construct and I noted it is only used by astronomers, not historians.
However, the statement that it cannot exist mathematically is not necessarily true. If it were true, then how could there be a temperature of 0 in either the Celsius scale or the Fahrenheit scale?
In practice, the range between -0.5 to +0.5 is rounded to zero and covers as much of the scale as -1 or +1 but is between them, not artificially added to them for no reason.
So the argument is similar, a year zero could exist in theory. The real point is that people alive around the years 1 B.C. to 1 A.D. (if you accept no year zero) did not know they were living in years that would be designated with these numbers. That only became true several centuries later when the early Church decided to number years not from the founding of Rome but from the birth of Jesus. Their first stab at it incorporated a four year error.
But nobody with the possible exception of Jesus knew that 1 A.D. was 1 A.D. at the time. So whether they thought the previous year was zero or 1 B.C. is a moot point, they never thought about it. The early church may not have either, I would imagine the whole concept of years B.C. came into usage much later when historians started to attempt to form chronologies.