Question: (3) For every sequence (an ) in R prove the following statements: (i) There exist strictly increasing sequences (n; ) and (n; ) in N

(3) For every sequence (an ) in R prove the following statements: (i) There exist strictly increasing sequences (n; ) and (n; ) in N so that limj-+0 On; = lim inf-+0 an and lim;-+0 on, = lim sup,-+ Un. (ii) lim inf-+oo an = - lim sup-+(-an)

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