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(i) Va, b = K, [a ≥ b ⇒ a +1≥ b + 1]. (ii) c € K, Va, b € K, a + b > c. (iii) Va, b = K, 3c € K, a + b > c.

(i) Va, b = K, [a ≥ b ⇒ a +1≥ b + 1]. (ii) c € K, Va, b € K, a + b > c. (iii) Va, b = K, 3c € K, a + b > c.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.1: The Field Of Real Numbers
Problem 7TFE: Label each of the following statements as either true or false. The field of rational numbers is...
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In each of the questions below identify the statement that does not hold in a complete ordered field K and provide a counterexample, or an argument as to why it does not hold.
Transcribed Image Text:In each of the questions below identify the statement that does not hold in a complete ordered field K and provide a counterexample, or an argument as to why it does not hold.
(i) Va, b = K, [a ≥ b ⇒ a +1≥ b + 1]. (ii) c € K, Va, b € K, a + b > c. (iii) Va, b = K, 3c € K, a + b > c.
Transcribed Image Text:(i) Va, b = K, [a ≥ b ⇒ a +1≥ b + 1]. (ii) c € K, Va, b € K, a + b > c. (iii) Va, b = K, 3c € K, a + b > c.
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