A3 - . 3. State the Axiom of Completeness . The Axiom of...

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1. Let A be a subset of R and s a real number . (a) s to be an upper bound for A . s is an upper bound for A if a s for every element a in A . (b) s to be the least upper bound for A . s is the least upper bound for A if s is an upper bound for A , and s b for any upper bound b of A . 2. Compute, without proofs , f m=n : m;n 2 N and m < 2 n g The supremum is 2 , the in&mum is
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Unformatted text preview: . 3. State the Axiom of Completeness . The Axiom of Completeness is given on page 14 of the text. It says that every nonempty set of real numbers that is bounded above has a least upper bound. 4. Is the statement , ± Every nonempty set of real numbers is bounded above ,² true or false ? If false , explain why . It³s false. The subset N of R is nonempty but is not bounded above....
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This note was uploaded on 05/26/2010 for the course MATH maa 4200 taught by Professor Dr. during the Spring '08 term at Miami University.

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