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Why power set of $Omega$ (set of all outcomes) can't always be used as field in probability space ($Omega,mathcal{F}, P$)?

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Topological proof for the unsolvability of the quintic

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algebraic topology quintic equations

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Degree of a determinant

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Are basic feasible solutions, vertices, and extreme points equivalent for semidefinite programs (SDPs)?

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optimization semidefinite programming

Find all functions $f:mathbb{R}^+to mathbb{R}$ such that $xf(xf(x)-4)-1=4x$

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