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Technically the 21st century began 1/1/2001

You are right. I remembered the new century/millennium celebrations in the year 2000, and based my comment on that.

Changed the title a little, hard to get it right :)

It's the 20th year of the 21st century. The 21st century began in 2001.

It's also the last year of the 202nd decade.

It's definitely 21st year of 21st century. 2001 was 1st year, not 0th :)