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Question: this is a multipart question please answer all parts of...

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This is a multi-part question. Please answer all parts of the question: b. Find an infinite collection of sets (Ai),1,2,3,... such that (i) Ai C R,i 1,2,3,...; (ii) each Ai is an open interval of length 1 (that is, A,-(ai , ai + 1) for some ai; and (iii) U 1 A,-(0, oo). (That is, the union of all the Ais is the set of all positive real numbers.) c. Find an infinite collection of sets (A),n 1,2,3,... such that (i) An C [-1/2, 1/2], n = 1, 2, 3, 1/n; and (iii) no 1 An = {0}. (ii) each An is an open interval of length d. *Find an infinite collection of sets (An),n -1,2,3,... such that (i) An C [0,1], n 1, 2, 3, An+1 C An, n = 1, 2, 3, , (ii) each An is an open interval of length 1/n; (iii) ; and (iv) に1 An = ø

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