DARTMOUTH COSC 030 - 01sets (10 pages)

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01sets



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01sets

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Pages:
10
School:
Dartmouth College
Course:
Cosc 030 - Discrete Math Computer Sci
Discrete Math Computer Sci Documents

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CS 30 Discrete Mathematics Professor Teaching Assistants Sagar Kale Head TA Yining Chen Chief grader Richard Rick Dionne Ninja Nan Hu Amit Chakrabarti Ninja Hang Christine Qi Ninja Shikhin Sethi Ninja The Language of Mathematics Math is not just a tool it is a way of communicating ideas It is a language We must Jirst become comfortable with it The building blocks of this language Sets Integers More general numbers rational real complex Functions Logic More advanced math sets are the only building blocks we need all else can be built from sets http www cs dartmouth edu cs30 Review of Sets A set is a collection of distinct objects These objects elements or members of the set If x is an element of the set S we write x S read x belongs to S or x is in S Example the set of fruits I like F apple banana fig mango pear apple is an element of F so apple F apricot is not so apricot F Review of Sets II An element either belongs to a set or does not No such thing as partially belonging to a set No such thing as number of copies of an element in a set Example set of letters in DARTMOUTH COLLEGE D A R T M O U H C L E G A C D E G H L M O R T U Finite and Infinite Sets The sets seen so far are all Jinite sets Number of elements cardinality of the set Notation S cardinality of set S E g F apple banana fig mango pear results in F 5 Not all sets are Jinite E g the set of all even natural numbers E 2 4 6 8 10 12 is an inJinite set Other inJinite sets N 1 2 3 4 the set of natural numbers Z 3 2 1 0 1 2 3 the set of integers Q 0 1 1 2 2 1 3 2 3 9 5 22 7 rational numbers R the set of real numbers includes 2 etc Describing a Set There are two main ways 1 Roster notation list out all the elements F apple banana fig mango pear 2 Set builder notation describe the property of a generic element of the set and write x some property of x F x x is a fruit and I like x Read F is the set of all x such that x is a fruit and I like x Other Interesting Possibilities A set with just one element is called



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