Some textbooks use set membership notation instead: f(x) ∈ O(g(x)). This makes sense if you think of O(g(x)) as the set of all functions with that upper bound.

Some textbooks use set membership notation instead: f(x) ∈ O(g(x)). This makes sense if you think of O(g(x)) as the set of all functions with that upper bound. However, the (abuse of) equality notation is often more convenient. For example, f(x) = x^2 + O(x) reads “f(x) is x^2 plus (something bounded by) a linear term”. Writing f(x) = x^2 + g(x) where g(x) ∈ O(x) is more of a hassle.