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Unformatted text preview: , that M is bounded below, and that sup S = inf M. 3. LetA be a negative real number. Use the Least Upper Bound Axiom to prove that there is an integer (necessarily negative) n such that n <A. 4. a) Give the ±N deﬁnition of lim n →∞ s n = s. b) Use the deﬁnition to prove that lim n →∞ 10 n +(1) n n = 10 . 5. Carefully prove that if lim n →∞ a n = a and lim n →∞ b n = b , where a and b are real numbers, then lim n →∞ ( a n + b n ) = a + b. 1...
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This note was uploaded on 11/15/2010 for the course MATH math 131 taught by Professor Kim during the Spring '10 term at UCLA.
 Spring '10
 Kim
 Math, Algebra

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