Midterm 1 Review

Midterm 1 Review - Math 117, F 09 Review Outline for First...

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Unformatted text preview: Math 117, F 09 Review Outline for First Midterm Definitions. sequence converge neighborhood bounded from above/below (a sequence or a set) bounded (a sequence or a set) convergent/divergent limit (of a convergent sequence) Cauchy sequence accumulation point lower/upper bound greatest lower bound / least upper bound infimum/supremum Least Upper Bound Property of R subsequence increasing/decreasing sequence monotone sequence Symbols. N, Z, Q, R {a n }∞ n=1 sup / inf Theorems. This is a list of the major theorems (and corollaries, etc.) that we have developed so far, with phrases labelling them. You don’t need to memorize the numbers of these theorems, just the statements. The numbers are just listed here to help you find things in the book. (Lemma, p.35) convergence in terms of neighborhoods (1.1) uniqueness of limits of sequences (1.2) convergent implies bounded (1.3) convergent implies Cauchy (1.4) Cauchy implies bounded (Lemma, p.39) alternate condition for an accumulation point (0.20) existence of greatest lower bounds (1.6) The Bolzano-Weierstrass Theorem (1.7) Cauchy implies convergent (1.8) sum of two convergent sequences (1.9) product of two convergent sequences (1.10) (1.11) (1.12) (1.14) (1.15) (1.16) bounding a sequence away from zero quotient of two convergent sequences inequalities between two convergent sequences convergence via subsequences convergence of bounded sequences convergence of monotone sequences ...
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Midterm 1 Review - Math 117, F 09 Review Outline for First...

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