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Unformatted text preview: âˆž i=1 A i = {0}. c) As I increases, the sets get larger: A 1 Ø¿ Ü£ 2 Ø¿ A 3 â€¦.. . All the sets are subsets of the set of positive real numbers R + , and every positive real number is included eventually, so U âˆž i=1 A i =R + . Because A 1 is a subset of each of the others, âˆ© âˆž 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:â€¦. â€¦ Ø¿ A 3 Ø¿ Ü£ 2 Ø¿ A 1 . Because A 1 includes all the others, U âˆž i=1 A i = (1, âˆž) (all real numbers greater than 1). Every number eventually gets excluded as I increases, so âˆ© âˆž i=1 A i = ] . Notice that âˆž is not a real number, so we cannot write âˆ© âˆž i=1 A i ={âˆž} 50. 001110 0000...
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 Spring '09
 Set Theory, Natural number

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