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Unformatted text preview: (vi) The product of an irrational number and an irrational number is irrational. (vii) If A = { r ∈ Q : r 2 < 3 } then lub A does not exist. 5. (5 points) Exhibit an irrational number between 7 9 and 8 9 . Give reasons. 6. (8 points) Let A = { x ∈ R : x ≥ 0 and x 2 < 3 } . Let v = lub A . Prove v 2 ≤ 3. [You may NOT assume Theorem 4.14, but you may assume FACTS 1,2,3]. 7. Suppose a and b are not both zero and a,b ∈ Q . (i) (5 points) Prove a 25 b 2 6 = 0. (ii) (5 points) Hence show that Axiom MIV holds for Q [ √ 5] := { a + b √ 5 : a,b ∈ Q } . 1...
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This note was uploaded on 06/03/2011 for the course MAS 3300 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

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