# lecture02 - MA1100 Lecture 2 Sets Set Notations Set...

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1 MA1100 Lecture 2 Sets Set Notations Set Relations Set Operations

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MA1100 Lecture 2 2 Sets A set is a well defined collection of objects The set of all natural numbers The set of all rational numbers The set of all real numbers Example (Standard sets) R Q N The set of all integers Z The set of all irrational numbers I Z + The set of all complex numbers C The set of all positive real numbers R +
MA1100 Lecture 2 3 Sets A set is a well defined collection of objects 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 positive real numbers less than 10 Example (Sets with underlying conditions)

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Intervals of R Interval notation Range Name (a, b) a < x < b open interval [a, b] a § x § b closed interval [a, b) a § x < b half-open interval (- , b) x < b open ray [a, ) a § x closed ray (a, b] a < x § b half-open interval (a, ) a < x open ray (- , b] x § b closed ray
MA1100 Lecture 2 5 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

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MA1100 Lecture 2 6 Describing a Set By listing explicitly (Roster method) 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}
MA1100 Lecture 2 7 Describing a Set By listing explicitly (Roster method) The set of all even integers {…, -6, -4, -2, 0, 2, 4, 6, …} Infinite set with “ pattern 1111 , 123 4 ⎩⎭

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## This note was uploaded on 04/15/2010 for the course MATH MA1101R taught by Professor Vt during the Spring '10 term at National University of Singapore.

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lecture02 - MA1100 Lecture 2 Sets Set Notations Set...

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