CSE241 Recitation 1 Handout 1 Preliminary Summary: CSE241 Recitation 1 Handout 1 Preliminary A set is a collection of distinct objects. Sometimes a set might be large, or even with infinity elements. Thus we need a concise set notation { obj: certain condition holds for obj }. Some literatures may use `|' instead of `:'. Example 1. A few sets with either finite or infinity number of objects: · { n : integer n that is larger than 1000} · { n : integer n, there exists an integer k such that n = 2k} · { r : student r that is in CSE241 but not in CSE240 } is the universal quantification. It basically says that something is true for every thing/object. is the existential quantification, which basically means something is true for at least one object. Problem 1. Use the set notation and quantifications to denote following set of numbers: 1) All the even integers. 2) All the prime numbers. 3) All the composite numbers. 2 O, and Notations, A Review Definition 1. f(n) = O(g(n)) iff there exist positive constant c and n0 such that for every n n0, f(n) cg(n). The definition to is bypassed here. Definition 2. f(n) = (g(n)) iff there exist positive constant c1, c2 and n0 such that for every n n0, c1g(n) f(n) c2g(n). Fact 1. f(n) = O(g(n)) iffg(n) = (f(n)). Collections: Computer Technologies and Information Sciences