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Mathematics
General Math
Can chatgpt accurately calculate expected lengths in Pascal's triangle?
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[QUOTE="fresh_42, post: 6845785, member: 572553"] The set of proper normal subgroups ##S:=\{H\triangleleft G\,,\,\subseteq \}## is a partially ordered set and not empty, since ##\{1\}\in S.## If ##G## is finite then there is trivially a largest proper normal subgroup. If ##G## is infinite this follows from the AC, resp. from Zorn's lemma as the statement of choice in algebra: A partially ordered set, in which each chain has an upper limit, contains at least one maximal element. For those who are interested: [URL='https://www.amazon.com/dp/0387901388/?tag=pfamazon01-20']Hewitt, Stromberg Real and Abstract Analysis, GTM 25[/URL] has (theorem 3.12 page 14ff.) the proof of equivalence of [LIST] [*]Axiom of Choice [*]Tuckey's Lemma [*]The Hausdorff Maximality Principle [*]Zorn's Lemma [*]The Well-Ordering Theorem [/LIST] [/QUOTE]
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Mathematics
General Math
Can chatgpt accurately calculate expected lengths in Pascal's triangle?
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