Physicists and engineers use the phrase "order of magnitude" to refer to the smallest power of ten needed to represent a quantity. Two quantities A and B which are within about a factor of 10 of each other are then said to be "of the same order of magnitude, " written A~B. Hardy and Wright say a real function f(x) and positive function ϕ(x) with continuous variable x that tends to some limit are of the same order of magnitude, written using asymptotic notation as f≍ϕ, if A_1 ϕ

asymptotic | asymptotic notation | tilde