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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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