I've lined in New York City all my life. It's the best city on earth.
How many people live in New York? 
A few... 8,537,673 to be exact but some day's it feels like more. Have you ever came to the city? 
I've been to New York City.  How large is the metro area? How far does it extend? 
It's not that big but dose have 5 boroughs. Brooklyn, Queens, Manhattan, The Bronx, and Staten Island. I live in soho which is in Manhattan. 
Yeah but the metro area is spreads across three states. 
Real New Yorkers only consider the 5 boroughs to be NYC. 
Yes but the US federal government legally recognizes the metro area is much larger than that. 
We all know the government is clueless. I bet I know 8,537,673 that would agree with me. 
The government is merely a collection of people with similar background.  And in the case of city metro areas it is larger than an incorporated area. You need to read more about it.