hw3solutions

hw3solutions - i=1 A i = {0}. c) As I increases, the sets...

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SOLUTIONS TO HOMEWORK#3 (Total Point: 80) Section 1.6: 8 (points: 5), 18, 40 (points :10) Total point:25 Section 1.7: 12, 20 , 34 (points: 5) Total point:15
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Section 2.1: 6, 8, 20 (Points: 5) , 36 (Points: 10) Total points : 25 Section 2.2: 48 (points: 10) , 50(a) (points: 5) Total points : 15 48. a) As I increases, the sets get smaller: … ؿ A 3 ؿ ܣ 2 ؿ A 1. All the sets are subsets of A 1, which is the set of positive integers, Z + . It follows that U i=1 A i = Z + . every positive integer is excluded from at least one of the sets (in fact from infinitely many), so ∩ i=1 A i = ] . b)All the sets are subsets of the set of natural numbers N (the nonnegative integers). The number 0 is in each of the sets, and every positive integer is in exactly one of the sets, so U i=1 A i =N and ∩
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Unformatted text preview: i=1 A i = {0}. c) As I increases, the sets get larger: A 1 2 A 3 .. . All the sets are subsets of the set of positive real numbers R + , and every positive real number is included eventually, so U i=1 A i =R + . Because A 1 is a subset of each of the others, i=1 A i = A 1 = (0,1) (tne interval of all real numbers between 0 and 1, exclusive). d) This time , as in part (a), the sets are getting smaller as i increase:. A 3 2 A 1 . Because A 1 includes all the others, U i=1 A i = (1, ) (all real numbers greater than 1). Every number eventually gets excluded as I increases, so i=1 A i = ] . Notice that is not a real number, so we cannot write i=1 A i ={} 50. 001110 0000...
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hw3solutions - i=1 A i = {0}. c) As I increases, the sets...

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