Concerning the formal definition of Big Oh.  

> f(n) = O(g(n))

Why is it not: 

> f(n) = O(f(n))   

or   

> f(n) = O(n*f(n))

since for the Big Oh analysis, `f(n)=2n` and `g(n)=n` are identical?  

I am confused on defining the function `f(n)` using another function