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Unformatted text preview: x + y on division by 12 , x y = the remainder left by x y on division by 12 . Show that Z 12 is not a eld. Note that this can be done by showing that Z 12 does not satisfy at least one of the eld axioms, or alternatively by showing that Z 12 does not satisfy one of the properties that we proved (in class or in Problem 1 above) that a eld must satisfy. 3. Let x,y be positive real numbers. Prove the arithmeticgeometric mean inequality xy x + y 2 . Use only the order axioms of R (Section 1.4) and standard algebra. 1 4. Answer problem 1.6.2 in the textbook. 5. Let E R be a set for which max E exists. Prove that max E = sup E , or show a counterexample. 1 For a hint, see note 3 at the end of Chapter 1 in the textbook....
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This note was uploaded on 10/16/2011 for the course MATH 34 taught by Professor Wiley during the Winter '11 term at UC Merced.
 Winter '11
 Wiley
 Differential Equations, Calculus, Equations

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