Here is the definition I am going of of.

Letfandgbe real-valued functions defined on the same set of nonnegative real

numbers. Then

1.fis of order at leastg,writtenf(x)is Big-Omega(g(x)), if, and only if, there exist a

positive real numberAand a nonnegative real numberasuch thatA|g(x)|≤ |f(x)| for all real numbersx>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.