Lecture_9 - MA1100 Lecture 9 Sets Set Notations Set Relations Set Operations 1 Sets A set is a well defined collection of objects Example The set

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
1 MA1100 Lecture 9 Sets Set Notations Set Relations Set Operations
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MA1100 Lecture 9 2 Sets A set is a well defined collection of objects The set of all positive integers Z + The set of all rational numbers Q The set of all integer solutions of x 2 = 9 The set of all rational numbers of the form 1/n where n is a positive integer The set of all real numbers R The set of all positive real numbers less than 10 Example
Background image of page 2
MA1100 Lecture 9 3 Elements of a Set Let A denote a set. if y is an object that belongs to this set A, we say y is an element of A and write y œ A . If y is not an element of A, we write y A Example 1.5 œ Q 2 Q A set with finitely many elements is called a finite set . The number of elements in a finite set A is called the cardinality of A and is denoted by |A|. Example A = {a, b, c} |A| = 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MA1100 Lecture 9 4 A strange “set” Let T be the “set” containing every set A such that A does not belong to itself We can use set to refer to almost any collection of objects: •Theseto f all animals •Theseto f all NUS students Let S be the “set” of all sets. Then S œ
Background image of page 4
MA1100 Lecture 9 5 Roster Method Roster method is a way to specify elements of a set by listing . This method works for small finite sets sets with elements having a fixed pattern The set of all integer solutions of x 2 = 9 The set of all positive integers less than 10 {-3, 3} {1, 2, 3, 4, 5, 6, 7, 8, 9} {1, 2, 3, …, 9}
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MA1100 Lecture 9 6 Roster Method The set of all even integers {…, -6, -4, -2, 0, 2, 4, 6, …} Infinite set with “ pattern Roster method is a way to specify elements of a set by listing . L 4 1 3 1 2 1 1 1 , , , , The set of all rational numbers of the form 1/n where n is a positive integer
Background image of page 6
MA1100 Lecture 9 7 Set Builder Notation The set of all positive real numbers less than 10 We can describe the set using set builder notation { x œ R | 0 < x < 10 } underlying set underlying condition If we denote the set of positive real numbers as R + we can also write the set builder notation as { x œ R + | x < 10 } Not all sets can be described using roster method:
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MA1100 Lecture 9 8 Set Builder Notation { x œ U | P(x) } General form U : underlying set for the variable x P(x): underlying condition in terms of x that describe the elements
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/19/2012 for the course SCIENCE MA1100 taught by Professor Forgot during the Fall '08 term at National University of Singapore.

Page1 / 33

Lecture_9 - MA1100 Lecture 9 Sets Set Notations Set Relations Set Operations 1 Sets A set is a well defined collection of objects Example The set

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online