Analysis

Analysis - Kimberly Zhang Analysis Useful Things |a + b|...

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Unformatted text preview: Kimberly Zhang Analysis Useful Things |a + b| |a| + |b| | |a| |b| | |a b| Definitions L is an upper bound for S iff L s for all s S. L is the least upper bound for S iff L is an upper bound for S and if M is also an upper bound for S, then L M. A sequence {a n } converges to a real number A iff for each > 0, there is a positive integer N such that for all n N, we have |a n A| < . A sequence {a n } is Cauchy iff for any > 0, there is a positive integer N such that for all m,n N, we have |a m a n | < . Let S be a set of real numbers. A real number A is an accumulation point of S iff every neighborhood of A contains infinitely many points of S. Axiom of Completeness: Any nonempty subset of R that is bounded above has a least upper bound. Monotone Convergence Theorem: A monotone sequence is convergent iff it is bounded. Let : D R with x an accumulation point of D. Then f has a limit at x iff for each > 0 there is a > 0 such that if 0 < |x x...
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This note was uploaded on 09/13/2009 for the course 640 311 taught by Professor Staff during the Spring '08 term at Rutgers.

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Analysis - Kimberly Zhang Analysis Useful Things |a + b|...

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