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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.

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.

Advanced Engineering Mathematics
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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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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