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Unformatted text preview: ² : (b) Show that C with the relation ² satis&es all the order axioms except one. Which axiom does it not satisfy? (For the axiom it will not satisfy do not try a general proof, it is enough to give a counter example.) 3. Using the order &eld axioms, prove the following: (a) If x ³ y and < x; then y & 1 ³ x & 1 : (b) ( ± 1) ´ x = ± x 4. If F is an ordered &eld, we showed in class that it has a subset Q F that looks like Q consisting of all elements of the form p F ´ q & 1 F where p; q are integers, q 6 = 0 and n F = 1 F +1 F + ::: +1 F ( n times) for a positive integer n: Use the order axioms and other results we proved in class to show that 1 F ³ 5 F ´ 3 & 1 F ³ 2 F : 1...
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This note was uploaded on 06/25/2010 for the course MATH MATH 301 taught by Professor Alberterkip during the Fall '08 term at Sabancı University.
 Fall '08
 ALBERTERKIP
 Math, Matrices

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