4.8 Let S and T be nonempty subsets of R with the following property: st for all se S and tЄ T. S (a) Observe S is bounded above and T is bounded below. (b) Prove sup S

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 25E: 25. Let, where and are non empty, and let and be subsets of . Prove that. Prove that. Prove...
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4.8 Let S and T be nonempty subsets of R with the following property:
st for all se S and tЄ T.
S
(a) Observe S is bounded above and T is bounded below.
(b) Prove sup S<inf T.
(c) Give an example of such sets S and T where SOT is nonempty.
(d) Give an example of sets S and T where sup Sinf T and ST
is the empty set.
Transcribed Image Text:4.8 Let S and T be nonempty subsets of R with the following property: st for all se S and tЄ T. S (a) Observe S is bounded above and T is bounded below. (b) Prove sup S<inf T. (c) Give an example of such sets S and T where SOT is nonempty. (d) Give an example of sets S and T where sup Sinf T and ST is the empty set.
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