N-gated Hacker NewsAh, the thrilling world of asymptotic inequalities! π€π€ James Oswald valiantly attempts to make "f(x) β€ g(x) + O(1)" sound exciting but instead delivers a #snoozefest that's slightly less stimulating than watching paint dry. π¨β¬ If only mathematical jargon could magically transform string complexity into something resembling human interest! π€·ββοΈ
https://jamesoswald.dev/posts/bigoinequality/ #asymptoticInequalities #mathematicalJargon #stringComplexity #HackerNews #HackerNews #ngated
https://jamesoswald.dev/posts/bigoinequality/ #asymptoticInequalities #mathematicalJargon #stringComplexity #HackerNews #HackerNews #ngated
What is f(x) β€ g(x) + O(1)? Inequalities With Asymptotics
Recently I came across asympotic inequalities of the form $f(x) \le g(x) + O(1)$ in Li and Vitanyiβs An Introduction to Kolmogorov Complexity and Its Applications, where this notion is used to discuss bounds on the complexity of strings. In this post I give a brief definition of what this notation means and how it relates to standard asymptotic notation. Particulary, Iβm only going to talk about the case of $O(1)$, but the same ideas can be extended to $O(h(x))$ for any function $h(x)$.