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lecture02&iuml;&frac14;ˆcomplete&iuml;&frac14;‰

# lecture02&iuml;&frac14;ˆcomplete&iuml;&frac...

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1 MA1100 Lecture 2 Sets Set Notations Set Relations Set Operations Chartrand: section 1.1 – 1.3

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MA1100 Lecture 2 2 Announcement ± Chartrand’s book available at Co-op now . ± Tutorial balloting starts today (NUS students only) ± Introductory handouts ± Start looking for your lecture quiz buddy (LQB) today. Settled by next week. ± Mock-up lecture quiz for lecture 2, 3, 4.
MA1100 Lecture 2 3 Sets A set is a well defined collection of objects The set of all natural numbers The set of all rational numbers We can determine whether or not certain object belong to the set . 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 + Zahlen (means “numbers” in German) In this module, 0 is not included in N wiki

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MA1100 Lecture 2 4 Sets A set is a well defined collection of objects We can determine whether or not certain object belong to the set . 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)
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 (a, b] a < x § b half-open interval (a, ) a < x open ray (- , b) x < b open ray [a, ) a § x closed ray (- , b] x § b closed ray Include all the real numbers within the range

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MA1100 Lecture 2 6 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 . Example A set which is not finite is called an infinite set . The set of all integer solutions of x 2 = 9 N, Z, Q, R, C [a, b] finite infinite infinite (set) finite interval
MA1100 Lecture 2 7 Cardinality The number of elements in a finite set A is called the cardinality of A and is denoted by |A|.

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lecture02&iuml;&frac14;ˆcomplete&iuml;&frac...

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