I regret to inform you that in the Gregorian tradition you are incorrect. If you are referring to some other tradition, please provide further explanation.
Is it? The first century spanned year 1 to 100 (there was no year zero). So the XX00 year is considered to be part of the preceding century. Thus 2021 is indeed the 21st year of the 21st century.
One definition of "first" is "preceding all others" [0], so something with an index of 0 would still be the first item.
Apparently the definition of "zeroth" is "being numbered 0 in a series" [1], so something with an index of 0 could be both the "first" and the "zeroth" item...
However, another definition of "first" is "one that is number one in a series", so the headline of this post is both accurate and inaccurate, depending on which definition you want to use, I suppose.
Yea it's mostly a joke and shows how a lot of this is contextual. I personally consider 1999-2000 the transition into the 21st century. Arguments otherwise are little more than awkward pedantry. Year 2021 could be seen as either the 21 or 22 year of the 21st century but i'm willing to side with the validity of OP's title.
Sorry, I should have been more clear. In 2000 there was a big debate over whether that was the first year of the new century. I sincerely thought that it had been settled long ago. Year 0 never existed (Christ is conventionally born on year 1 [1]), and the first hundred years (first century) go from 1 to 100. The second hundred years (second century) begin in 101, and so on.
Another way to put it is that we don't number calendar years the way we do birthdays/ages.¹ Which probably accounts for some of the popular confusion here.
Your 23rd birthday is at the end of your 23rd year, and you're "23" from then until the 24th birthday. But you're actually progressing through your 24th year at that point.
Conversely, during the year called "2000" we were in the 2000th year. We completed 2000 years at the end of it. Upon which we started marking progress in the 2001st year.
This makes sense. That being said, convention is very useful until it is broken for further optimization and setting better standards. I'm just not sure that a debate over "when it really started" is useful in that specific applications can define the start and end based upon what is needed rather than what is right, wrong, or accepted by convention. One exception to this is that non-specialists or students may learn something from the debate (provided it is public). A more useful debate would be whether or not we should rid ourselves of daylight savings time!
