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Unformatted text preview: x < for every > 0, then x 0. (8) Complete the partial discussion in Rudins Step 6 (pp. 1920) establishing multiplication and its properties in R + . (9) Let E and F be nonempty subsets of R . Suppose that for all x E and y F we have x < y . Prove that sup E inf F. Can be replaced by < ? (10) Is the set = { x Q : x 2 < 3 } a Dedekind cut? If so, prove that 2 = 3. If not, nd a Dedekind cut whose square is 3. (11) Theorem 1.20 in Rudin is proven abstractly as a consequence of the leastupperbound property. Give a concrete proof using the construction of R by Dedekind cuts. 1...
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This note was uploaded on 04/11/2008 for the course ECON 150 taught by Professor Eduardofaingold during the Spring '08 term at Yale.
 Spring '08
 EduardoFaingold
 Microeconomics

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