The A.D. (Latin, Anno Domini, In the Year of Our Lord) system was devised before «origin 0 counting» was invented. The year during which Jesus was (incorrectly) assumed to have been born was numbered 1. (The preceding year was 1 B.C.) So the 1st century was 1 to 100, the 2nd was 101 to 200, the 20th is 1901 to 2000. This is standard terminology no matter how much some of you may dislike it. However, «a» century is any span of 100 years; so if you want to celebrate the end of «the century», meaning the 1900's, on December 31, 1999, nobody will stop you. It just isn't the end of the «20th century A.D.».