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Unformatted text preview: ∈ R , sup { f ( x ) + c ; x ∈ A } = c + sup { f ( x ); x ∈ A } . Problem 3 (10 points) Print your name: Show that the sequence a n = (1) n p 2 + 1 n 2 P , n = 1 , 2 , . . . is not a Cauchy sequence. Problem 4 (10 points) Print your name: Let S be a set of sequences of rational numbers such that each sequence has a Fnite number of nonzero terms. Prove that S is countable. Problem 5 (10 points) Print your name: Let { a n } be a monotone sequence of real numbers which has a convergent subsequence. Show that { a n } converges....
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 Fall '08
 hitrik
 Math, Rational number, Cauchy sequence

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