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What does the punchline reveal about Jim smiley
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Mar 26, 2022
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What does the punchline reveal about Jim smiley
English
high-school
Ajit Panigrahi
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Answer:
what?
Step-by-step explanation:
what does this even mean
Benedict Lewis
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Mar 30, 2022
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Benedict Lewis
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The Cut Property of the real numbers is the following: If A and B are nonempty, disjoint sets with A∪B = R and a < b for all a ∈ A and b ∈ B, then there exists c ∈ R such that x ≤ c whenever x ∈ A and x ≥ c whenever x ∈ B. (a) Use the Axiom of Completeness to prove the Cut Property. (b)Show that the implication goes the other way; that is, assume R possesses the Cut Property and let E be a nonempty set that is bounded above. Prove sup E exists. (c)The punchline of parts (a) and (b) is that the Cut Property could be used in place of the Axiom of Completeness as the fundamental axiom that distinguishes the real numbers from the rational numbers. To drive this point home, give a concrete example showing that the Cut Property is not a valid statement when R is replaced by Q.
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