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.
The Douay Rheims includes:
“AN HISTORICAL AND CHRONOLOGICAL INDEX TO THE OLD TESTAMENT”
The chronology followed in the index is:
“...according to the more general Opinion of Divines and Chronologers”.
A note further indicates:
“A.M. signifies, Anno Mundi: that is, In the year of the World.”
Indicated as occurring in the year A.M. 1:
Creation of Heaven and Earth, including the creation of the first Patriarch, that being, of course, Adam.
Indicated as occurring in the year A.M. 130:
Birth, to Adam and Eve, of the second patriarch, that being, third-born Seth.(Firstborn son Cain’s line having subsequently been extinguished by the flood (Noah being of the line of Seth), and second-born son Abel, slain by Cain, having apparently been without issue.)
By the way, the aforementioned flood is indicated as having occurred in A.M. 1656.
Next, the Douay Rheims includes:
AN HISTORICAL AND CHRONOLOGICAL INDEX TO THE NEW TESTAMENT
The noted New Testament index does not use A.M., but instead uses “A.D.”
A.D., or course, is “Anno Domini”, meaning, in the year of our Lord.
The first entry in the New Testament index is “Christ is born at Bethlehem. Luke 2.
The year of this event is indicated as A.D. 1.
“However, the statement that it cannot exist mathematically is not necessarily true.”
This Guy will concede that labeling of years is by convention.
From a mathematical perspective, however, the only convention that facilitates calculation, in terms of, say, the basic mathematical functions of addition and subtraction, is the one that abuts year 1 “B.C.” to year 1 “A.D.”, the center dot in the number line representing midnight, that midnight being the one that abuts (falls directly between) March 24, 1 B.C. and March 25, 1 A.D.
March 25th is the Feast of the Annunciation.
Until relatively recently, the Feast of the Assumption was recognized as New Year’s Day.
The Annunciation comprehended (comprehends?) the Incarnation.
The Incarnation, of course, being the very first moment of Christ’s human life on earth.