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Consider the following proof that every sequence ${x_n}_n$ in $mathbb R$ has a monotone subsequence.Proof: Let us call a positive integer $n$ a peak of the sequence...
Asked on 01/03/2021 by MathMan
2 answerA function $f: Bbb C_{infty}to Bbb C_{infty}$ is biholomorphic if $f$ is bijective, holomorphic and $f^{-1}$ is holomorphic on $Bbb C_{infty}$, where $Bbb C_{infty}$ is...
Asked on 01/03/2021
1 answerLet $Omega$ be a domain with smooth boundary $partial Omega$, $bar{Omega}$ is compact. The Neumann problem:$f in C^{infty}(bar{Omega})$,$gin C^{infty}(partial bar{Omega})$. Find a function $varphi...
Asked on 01/03/2021 by Xingying Li
1 answer$M$ is the intersection of 3 cevians in the triangle $ABC$. $$AB_1=x,~CA_1=y,~BC_1=z.$$ it can be...
Asked on 01/03/2021
2 answerPlayers $A$ and $B$ decide to play chess until one of them wins or ties $5$ times in a row. Assume games are independent, where $A$...
Asked on 01/02/2021 by Daisy Otaku
1 answerHere is the question I want to answer: Let $G$ be a finite group such that 3 does not divide $|G|$ and such that the identity $(xy)^3...
Asked on 01/02/2021
0 answerThis is the proof of Theorem 4.19. in Joseph J. Rotman „An Introduction to Algebraic Topology“. We want to show that $H_n(X)=0$ for all $n>0$ and $X$...
Asked on 01/02/2021 by Const
1 answerSay we have f(x) such that, f(x) = x^2 (Just an example maybe any other function too e.g: x^6, x^(-14) etc.) and we have, g(x) such that, g(x) = -x^2...
Asked on 01/02/2021 by Clown
0 answerI'm given the following question and am coming up with a different answer from the book. if $sec(a) = frac{x}{4}$ for $0 < x < frac{pi}{2}$ , find...
Asked on 01/02/2021 by maybedave
0 answerI found proofs in books (for example Oksendal's) where there is a process $S_t$ which satisfies $mathrm E[S_t^2]=0$ for all $t$. Based on this, a conclusion is...
Asked on 01/02/2021 by Tohiko
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