Why are the years of the 21st century numbered 20?

A long time confusion factor for me. When presented with "umpteenth century" in the text I always had a mental hangup. Why are the years of the umpteenth century always numbered umpteen minus one? E.G. the years of the tenth century are numbered 900 to 999, the years of the twentieth century are numbered 1900 to 1999.
It's because we don't have a zeroth century. The year and century numbering system goes back before the invention of zero, and even today we have trouble with the notion of a zeroth anything.
In the case of century dating, it got started early. It was natural to refer to the years between the birth of Christ and the year 99 AD as the first century. It still does, only computer programmers would dare call it the zeroth century. Once you call years 1 to 99 the first century, then you HAVE to call the years 100 thru 199 the second century. And there we go, and the confusion persists into the twenty-first century (years 2000 thru 2099)