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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)).


Source: Agrawal, Kunal - Department of Computer Science and Engineering, Washington University in St. Louis


Collections: Computer Technologies and Information Sciences