Here is the definition I am going of of.
Let f and g be real-valued functions defined on the same set of nonnegative real
1. f is of order at least g, written f(x) is Big-Omega(g(x)), if, and only if, there exist a
positive real number A and a nonnegative real number a such that A|g(x)| ≤ | f (x)| for all real numbers x > a.
So I am wondering why the constant A is multipled by g(x). Is it basically saying, "hey, at a certain point, it doesnt matter what you multiply g(x) by, because f(x) is so big that its gonna always be bigger then the multiple of g(x)".
Perhaps if someone could explain why x^2 is not Big-Omega(x) and that would help. I get how to solve problems it is jus the intuition I am missing.