What is f(x) ≤ g(x) + O(1)? Inequalities With Asymptotics
Summary
The post explains what the one-sided asymptotic bound f(x) ≤ g(x) + O(1) means, contrasting it with the standard two-sided Big-O form. It defines f(x) = g(x) + O(1) and shows that the one-sided version provides an upper bound for large x, while the two-sided bound implies both upper and lower bounds; formal definitions and intuition are provided.