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 Oct 18 comment Proving that $U(n)\subset SO(2n)$ Oh, that was elegant!! Thank you. Jul 31 comment How following matrices equation is solved? What do the $[]$ mean? Jul 2 comment Show that $A^k$ has eigenvalues $\lambda^k$ and eigenvectors $v$. I find your proof more simple, more direct, more general and more obvious, thus much better. Jun 19 comment Why are these curves' points called rational? Thanks for the answer and explanation Jun 19 comment Why are these curves' points called rational? Ok, thank you very much for the answer and the example. Which by the way... is it right? $i^4+i^4=2=\sqrt 2^4=4$? Should the curve have a $2$ coefficient multiplying the $x$ and $y$ terms? Jun 17 comment Proposed proof of topological result Other than that, I find it perfect. Try to separate paragraphs though, it's a bit hard to read. Jun 17 comment Proposed proof of topological result What's $(B,d)$ and $(A,d)$? Jun 12 comment Solutions for $|x^2-5x+2|=4$ @BetterWorld That means they should also come as a solution when you consider the negative sign of the modulus, try it. You should discard those solutions when you get the from the positive values, and when consider the negative, $x=1$ should come out again. Jun 12 comment Solutions for $|x^2-5x+2|=4$ @BetterWorld That just means they're not solutions, because they fail to satisfy the hypothesis that $x^2-x-1$ is positive, on which the solution depends. Jun 12 comment Solutions for $|x^2-5x+2|=4$ You're very welcome! :) No need for sirs. Jun 11 comment Choosing $8$ shoes from $20$ different pairs of shoes to get at least two pairs @Dargenn My result is $p=0.43$, and so the solution would be $0.57$. Jun 11 comment Choosing $8$ shoes from $20$ different pairs of shoes to get at least two pairs @Dargenn I'm sorry, $P$ should be $P=40\cdot39\cdot38\cdot\ldots\cdot33$, and this solution considers a different case the same set of shoes dissordered, so it's incomplete. You can divide by the number of permutations of the $8$ chosen shoes. Jun 10 comment What is the limit of the below functions when n tends to inifinity? First of all, welcome. Second, you shouldn't expect anyone here to do this for you. You must first expose what you know, what you have tried, and the problems you have doing these. Third, always try to format mathematical expressions, I did for you, please see the code to see how. Jun 10 comment The most efficient way to find a minimal value in a 2 dimensional matrix. @user3697176 I will add that. Jun 10 comment Basis of $\mathbb{Q}[\sqrt[3]{2}]$ Can you express any element of the ring as a linear combination of those three? Are succesive values of $2^{1/3}$ contained in the ring? Jun 10 comment The shortest path in a metric space with a given metric @SiXUlm Have in mind what Alex said. The above is only valid for manifolds with a differentiable structure. Those are the easiest to visualize though, so you should start with them. Jun 9 comment Continuous homorphisms between topological groups. The main difference with topological continuity is that this (the one you expose) only requires to be so for neighbourhoods of the identity of the group. That is a big difference. Jun 6 comment Coordinates on the sphere not global? It's hard to say. Could you give the source of the book? In principle the only two points on the sphere with coordinates not entirely defined are the poles, for which there is no well defined longitude. Jun 6 comment how to know in which range $\cos^{2}\theta$ $\le$ $\sin^{2}\theta$? @Sten Thanks for pointing out! Jun 6 comment How to prove that the Kronecker delta is the unique isotropic tensor of order 2? wow, whole answer in math mode :D