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Mathematics
General Math
Can chatgpt accurately calculate expected lengths in Pascal's triangle?
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[QUOTE="Infrared, post: 6845396, member: 467682"] 3. Looks true. The imaginary part of such a holomorphic function is harmonic and vanishes on the unit circle and so vanishes everywhere in the interior (for example, by Green's identities). By Cauchy-Riemann, the real part is constant there. So ##f## is constant inside the unit circle and hence everywhere 2. You need to assume ##G\neq\{1\}.## Take ##H## to be a maximal proper normal subgroup, which obviously exists if ##G## is finite. By a correspondence theorem, the normal subgroups of ##G/H## are of the form ##A/H## where ##H\subseteq A\subseteq G## and ##A## is normal in ##G,## so ##A/H## is either trivial or the whole quotient ##G/H##, meaning ##G/H## is simple. Finiteness is not required: ##\mathbb{Z}/2\mathbb{Z}## is simple. Note: By Zorn's lemma, I think every group should have a maximal normal proper subgroup. I don't think finiteness is required. (Edit: this last part is wrong as I later realize) [/QUOTE]
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Mathematics
General Math
Can chatgpt accurately calculate expected lengths in Pascal's triangle?
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