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# sets - CS 70 Fall 2006 Discrete Mathematics for CS...

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CS 70 Discrete Mathematics for CS Fall 2006 Papadimitriou & Vazirani Lecture 1 Introduction to Sets A set is a well defined collection of objects considered as a whole. These objects are called elements or members of a set, and they can be anything, including numbers, letters, people, cities, and even other sets. By convention, sets are usually denoted by capital letters and can be described or defined by listing its elements and surrounding the list by curly braces. For example, we can describe the set A to be the set whose members are the first five prime numbers, or we can explicitly write: A = { 2, 3, 5, 7, 11 } . If x is an element of A , we write x A . Similarly, if y is not an element of A , then we write y negationslash∈ A . Two sets A and B are said to be equal, written as A = B , if they have the same elements. The order and repetition of elements do not matter, so { red, white, blue } = { blue, white, red } = { red, white, white, blue } . Sometimes, more complicated sets can be defined by using a different notation. For example, the set of all rational numbers denoted by Q can be written as: { a b | a , b are integers, b negationslash = 0 } . In English, this is read as “the set of all

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sets - CS 70 Fall 2006 Discrete Mathematics for CS...

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