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Unformatted text preview: ** n s j =1 j 2 = n ( n + 1)(2 n + 1) 6 Note: This is book problem 3. 4. Suppose that S is a nonempty set of real numbers that is bounded. (a) Prove that inf S sup S . * (b) Why is it necessary that S be nonempty and bounded? * Note: Part (a) is book problem 13. 5. (a) Give an example of a set S of numbers that is nonempty and bounded above but has no * maximum. (b) Prove that a set S of numbers has a maximum i it is bounded above and sup S S . ** Note: This is book problem 15 reorganized. 6. Dene S = b x R v v x 2 < 2 x B . (a) Show that S is nonempty. * (b) Show that S has an upper bound. * (c) Which theorem can you apply and what is the conclusion? * (d) Conjecture a value for sup S . * (e) Show that sup S equals this value. ** Note: This is book problem 19 modifed and expanded....
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This note was uploaded on 02/27/2012 for the course MATH 2 taught by Professor Staff during the Spring '08 term at Maryland.
- Spring '08