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For probability triple $(mathbb{R}, mathcal{B}(mathbb{R}), mu)$ prove that for a random variable $X$, if $mu(X>0)>0$, there must be $alpha>0$ s.t. $mu(X>alpha)>0$. So if $X$...
Asked on 01/01/2022
2 answerProve or disprove that if $$prodlimits_{x=2}^{infty} f(x)=0$$ and $f(x)neq0$ for any $xgeq0$ then $$prodlimits_{x=2}^{infty} f(xvarphi)=0$$ for any constant $varphigeq2$ This seems true but I'm not...
Asked on 01/01/2022 by Smorx
3 answerThe motivation is an object which generalizes the notion of percentages. Consider the the set $mathbb{R}$ along with the usual binary addition operation $+$ and infinitely-many binary multiplication...
Asked on 01/01/2022
0 answerA diameter $AB$ and a chord $CD$ of a circle $k$ intersect at $M.$ $CE$ and $DF$ are perpendiculars from $C$ and ...
Asked on 01/01/2022
1 answerIn an $atimes b$ board, two players take turns putting a mark on an empty square. Whoever gets $cleq max(a,b)$ consecutive marks horizontally, vertically, or diagonally first wins....
Asked on 01/01/2022
1 answerI don’t know why contravariant and covariant vector field are named as such. contravariant literally means going against changing, or changing in the opposite way, covariant literally means changing with...
Asked on 01/01/2022
1 answerConsider a mapbegin{align}F:&[0~1]^mathbb{N}rightarrow mathbb{R}^mathbb{N}\&{x_k}rightarrow {y_k}=F{x_k}end{align}with the following properties:${y_k} rightarrow 0$ for all ${x_k}in[0~1]^mathbb{N}$$y_k=f(y_{k-1},x_k)$ for all $kinmathbb{N}$, where $f(cdot,cdot)$ is...
Asked on 01/01/2022 by Daniel Huff
0 answerI was learning the Krull-Schmidt theory and came across this concept and just can't understand what's it all about. A group endomorphism $fcolon Gto G$ is called normal iff...
Asked on 01/01/2022 by DarkGlimmer
2 answerA recursive algorithm that I'm working on is based on traversing an $n$-dimensional hypercube. The quantity associated to each vertex can be computed by combining the values of all...
Asked on 01/01/2022
0 answerLet $(M,g)$ be a Riemannian manifold of dimension $N$ with (Levi-Civita) connection $nabla$. I have seen the following definition of Christoffel symbols: For a given smooth moving...
Asked on 01/01/2022
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