of order

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let ϕ(n) or ϕ(x) be a positive function and f(n) or f(x) any function. Then Hardy and Wright define 1.f = O(ϕ) to mean that left bracketing bar f right bracketing bar 0, 3.f~ϕ to mean that f/ϕ->1, 4.f precedes ϕ to mean the same as f = o(ϕ), 5.f succeeds ϕ

almost all | asymptotic | big-O notation | big-theta notation | Landau symbols | little-O notation | order of magnitude | tilde