{"id":"big-o-notation","domain":"discrete","type":"Concept","title":"Big-O Notation","slug":"big-o-notation","url":"/mathematics/discrete/big-o-notation/","summary":"Describes algorithm growth rate as input size increases, ignoring constants. Originated in number theory (Bachmann 1894), standardized for CS by Knuth.","formal_definition":"f(n)=O(g(n)) if there exist C,n0 such that f(n)<=C*g(n) for all n>=n0","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Cormen, T.H., Leiserson, C.E., Rivest, R.L. and Stein, C. (2022). Introduction to Algorithms. 4th ed."},{"tier":1,"citation":"Knuth, D.E. (1976). Big Omicron and big Omega and big Theta. ACM SIGACT News, 8(2), 18-24."},{"tier":2,"citation":"Sipser, M. (2012). Introduction to the Theory of Computation. 3rd ed."},{"tier":3,"citation":"Fortnow, L. (2013). The Golden Ticket: P, NP, and the Search for the Impossible."}],"relationships":[{"type":"uses","target":"limit","label":"Limit — asymptotic behaviour"},{"type":"related_to","target":"recurrence-relation","label":"Recurrence Relation"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"2.1"}