One thing that you didn't actualy give is a defintion for "order of growth", which would explain why O(1)==O(2), and why O(2N+3) == O(N).
From a casual perspective, "order of growth" can be thought of as the shape of the worst-case growth curve, regardless of the slope of that shape. Even it a line indicating linear (i.e., O(N)) growth has a high slope, eventually--when the data set is big enough--it will be overtaken by an O(N2) curve. That's one of the pitfalls. People get seduced by the behavior of their code on small data sets, then get blindsided when they try a much larger data set and performance sucks.