February 23, 2026
Big O, Bigger Oh-No
What is f(x) ≤ g(x) + O(1)? Inequalities With Asymptotics
Tiny math symbol sparks big fight: equal sign or wink
TLDR: Oswald explains that “f ≤ g + O(1)” means f won’t exceed g by more than a fixed constant for large inputs. Commenters split: purists decry “f=O(g)” as sloppy, pragmatists say “just subtract g(x),” and educators offer analogies—proof that tiny notation can cause big arguments.
A bite-size post from James Oswald tried to calm the chaos: that mysterious “+ O(1)” just means “for big numbers, f doesn’t beat g by more than a small, fixed amount,” and the “≤” version is only an upper cap. But the comments turned a quiet math note into a full-on showdown. Team Pedant stormed in: josalhor fumed that writing “f = O(g)” is misleading because it looks like equality, not membership in a set. Team Pragmatist fired back with a vibes-only guide: dataflow basically said, “just subtract g(x) and chill,” and you get the idea. Then Team Educator arrived with friendly metaphors: edflsafoiewq compared it to “even + odd = odd,” meaning we’re talking about properties, not a specific number. The spicy meme of the day came from qsort, who joked that “mathematics runs on javascript,” so we swallow the awkward notation instead of throwing an error. In other words, this little symbol ignited a culture clash: purists want precise language, coders want readable rules, and teachers are trying to make peace with plain-English explanations. The result? Big O, big emotions—and a reminder that tiny symbols can trigger giant debates online.
Key Points
- •Standard Big O notation defines an upper bound: |f(x)| ≤ C|g(x)| for large x.
- •f(x) = g(x) + O(1) means the difference |f(x) − g(x)| is bounded by a constant for sufficiently large x.
- •From f(x) = g(x) + O(1), both upper and lower bounds follow: g(x) − C ≤ f(x) ≤ g(x) + C.
- •f(x) ≤ g(x) + O(1) specifies a one-sided upper bound: f(x) ≤ g(x) + C for large x.
- •f(x) = g(x) + O(1) implies f(x) ≤ g(x) + O(1), but not vice versa; ideas extend to O(h(x)).