Let A and B be nonempty subsets of R such that A is bounded above and B is bounded below and let A – B be defined by A - B= {a – b: a € A and bE B}. Prove that sup(A – B) = sup A – inf B.

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Author:Erwin Kreyszig
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Let A and B be nonempty subsets of R such that A is bounded above and B is bounded
below and let A – B be defined by A – B = {a – b : a € A and be B}. Prove that
sup(A – B) = sup A – inf B.
Transcribed Image Text:Let A and B be nonempty subsets of R such that A is bounded above and B is bounded below and let A – B be defined by A – B = {a – b : a € A and be B}. Prove that sup(A – B) = sup A – inf B.
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