On 15th August 1947, when the newborn India was 0 days old, we had our 1st independence day. That day we completed 0 years, and entered the 1st year of Independence. So, the calculation should be 1947-1946=1. Similarly, 2006-1946=60.
We have "completed" 59 years of Independence, and celebrated 60th Independence Day. And have entered into 60th year of Independence.
(Dont apply here the calculations you do to find out your age on your every birthday).