Without proving anything, determine if the following statements are true or false. For any false statements, give an counterexample. (a) A finite, nonempty set of real numbers always contains its supremum. (b) If a < L for every element a in the set A, then sup A < L. (c) If A and B are sets with the property that a < b for every a € A and b e B, then sup A < inf B. (d) If sup A = s and sup B = t, then sup(A+B) = s+t. Here and elsewhere, the set A+B is defined as A+B = {a+b:a € A, and b e B}. (e) If sup A < sup B then there is an element of B that is an upper bound for A.

Without proving anything, determine if the following statements are true or false. For any false statements, give an counterexample. (a) A finite, nonempty set of real numbers always contains its supremum. (b) If a < L for every element a in the set A, then sup A < L. (c) If A and B are sets with the property that a < b for every a € A and b e B, then sup A < inf B. (d) If sup A = s and sup B = t, then sup(A+B) = s+t. Here and elsewhere, the set A+B is defined as A+B = {a+b:a € A, and b e B}. (e) If sup A < sup B then there is an element of B that is an upper bound for A.

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter2: Working With Real Numbers

Section2.1: Basic Assumptions

Problem 40WE

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