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Test1Guide - DEFINITIONS N is an equivalence relation on...

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DEFINITIONS N is an equivalence relation on set A if o a ~ a for all a A o if a ~ b, then b ~ a for all a,b A o if a ~ b and b ~ c, then a~c for all a,b,c A The Completeness Axiom – If A is a subset of R, and A is bounded above, then sup (A) exists An infinite set is countable if there exists a f: N A where f is bijective. A subset B of R is dense in R if every interval (a,b) a < b contains an element of A. o Characteristics of Dense: 2200 r R , 5 a convergent sequence that converges to r A B R. A is said to be dense in B if given any b B, 5 a sequence of elements from A converging to b. Let A be a set. A sequence is a function f: N A o Sequences are ordered Let A and B be a non-empty sets. The Cartesian product is defined by o A x B = {(a,b) : a A, b B} We say {a n } converges to a if 2200ε , 5 a N N so that |a n – a| < ε for all n ≥ N Comparison Lemma : Suppose {a n } a. If there exists a c > 0, so that
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This note was uploaded on 11/29/2010 for the course CSC 873569 taught by Professor Roberts during the Spring '10 term at ASU.

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Test1Guide - DEFINITIONS N is an equivalence relation on...

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