Let A be a nonempty subset of R that is both bounded above and below and let B be a nonempty subset of A. Prove or disprove each of the following assertions. (a) inf(A) ≤ inf(B) ≤ sup(B) ≤ sup(A). (b) If inf(A) = sup(A), then A has exactly one element. (c) If inf(A) = inf(B) and sup(A) = sup(B), then A = B.

Let A be a nonempty subset of R that is both bounded above and below and let B be a nonempty subset of A. Prove or disprove each of the following assertions. (a) inf(A) ≤ inf(B) ≤ sup(B) ≤ sup(A). (b) If inf(A) = sup(A), then A has exactly one element. (c) If inf(A) = inf(B) and sup(A) = sup(B), then A = B.

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 5TFE: Label each of the following statements as either true or false. If a nonempty set contains an upper...

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