I am a programmer and have just started reading Algorithms. I am not completely convinced with the notations namely Bog Oh, Big Omega and Big Theta. The reason is by definition of Big Oh, it states that there should be a function g(x) such that it is always greater than or equal to f(x). Or f(x) <= c.n for all values of n >n0.

My doubt is the why dont we mention the constant value in the definition? For example. lets say a function 6n+4, we denote it as O(n). but its not true that the definition holds good for all constant value. this holds good only when c >= 10 and n >= 1. For lesser values of c than 6, the value of n0 increases. So why we do not mention the constant value as a part of the definition.