Explanation The completeness property of a real number state that allnon empty subset S of the real numbers that is bounded above has a supremum in real number R. And all non-empty subset S of the real numbers that is bounded below has an infimum in real number R. The completeness property many times called the least upper bound property. Example: let Z be a nonempty subset of real number R that is bounded below. Then there exist a lower bound m ∈ R such that m ≤ z , ∀ z ∈ Z . Let set T is the T = { − z : z ∈ Z } It observes that − z ≤ − m , ∀ − z ∈ T

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Ch. 2.1 - Prob. 1PS Ch. 2.1 - Prob. 2PS Ch. 2.1 - Prob. 3PS Ch. 2.1 - Prob. 4PS Ch. 2.1 - Prob. 5PS Ch. 2.1 - Prob. 6PS Ch. 2.1 - Prob. 7PS Ch. 2.1 - Prob. 8PS Ch. 2.1 - Prob. 9PS Ch. 2.1 - Prob. 10PS

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To state the completeness property.

Solution Summary: The author explains the completeness property of a real number, which states that all non-empty subset S of the real numbers that is bounded above has an infimum.

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Chapter 2 Solutions