Exercise 1.1.6, which asks for a proof that if A is a nonvoid subset of an ordered set S, and A is bounded above, and sup A exists in S but is not an element of A, then A contains a countably infinite subset.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...
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Please solve the second exercise with detailed explanations for each step thank you 

Exercise 0.3.4(b), which asks for an example of sets A and B, a function f: A → B, and subsets C and D of A such
that the image f(CD) is a proper subset of f(C) f(D), that is, f(CND) ≤ f(C) n f(D).
Exercise 1.1.6, which asks for a proof that if A is a nonvoid subset of an ordered set S, and A is bounded above, and
sup A exists in S but is not an element of A, then A contains a countably infinite subset.
Transcribed Image Text:Exercise 0.3.4(b), which asks for an example of sets A and B, a function f: A → B, and subsets C and D of A such that the image f(CD) is a proper subset of f(C) f(D), that is, f(CND) ≤ f(C) n f(D). Exercise 1.1.6, which asks for a proof that if A is a nonvoid subset of an ordered set S, and A is bounded above, and sup A exists in S but is not an element of A, then A contains a countably infinite subset.
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