higher analysis

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Author:
cbcarey
ID:
7749
Filename:
higher analysis
Updated:
2010-02-22 19:02:26
Tags:
higher analysis
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Description:
math theorems and definitions
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  1. bounded above
    a set A in R is bounded above if there exists a number b in R such that a is less than or equal to b for all a in A
  2. least upper bound
    • A real number s is the least upper bound for a set A in R if it meets the following two criteria:
    • (i) s is an upper bound for A
    • (ii) if b is any upper bound for A, then s is less than or equal to b
  3. axiom of completeness
    every nonempty set of real numbers that is bounded above has a least upper bound
  4. lemma of upper bound
    assume s is in R is an upper bound for a set A in R. Then, s=supA if and only if, for every choice of epsilon greater than 0, there exists an element a in A satisfying s-epsilon is less than a

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