Olivier Bégassat
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 Nov 16 comment Prove or Disprove: if $\lim\limits_{n \to \infty} (a_{2n}-a_n)=0,$ then $\lim\limits_{n \to \infty} a_n=0.$ What about the constant sequence $a_n=1$? Nov 8 comment First-order definition of “$f$ is continuous at $x$” using just $<$ @avid19 I see, is that the problem, that there are no such symbols in the language? But how is $\Bbb R$ to be understood in this context? Nov 8 comment First-order definition of “$f$ is continuous at $x$” using just $<$ Wouldn't something like \varphi(x)=\forall\epsilon >0~\exists\delta>0~\forall y~ (x-\delta0$for any$x,y,z$if and only if$c>0$and$\lambda+\frac{2c}{3}>0$? Sep 12 asked Existence of a measurable$\theta$such that$\frac{f(y)-f(x)}{y-x}=f'(\theta_{x,y})$? Aug 21 awarded general-topology Aug 12 awarded Enlightened Aug 12 awarded Nice Answer Aug 7 comment Describe a group$G$that acts on a set$X$of 4 elements such that the action of$G$has 2 orbits. An explicit example comes from geometry:$\mathrm{GL}_2(\Bbb F_2)$acts on$\Bbb F_2^2$, a four element set, and has two orbits. Similarly, yet less interestingly, the multiplicative group of units$\Bbb F_4^\times\simeq \Bbb Z/3\Bbb Z$acts on the four element set$\Bbb F_4$by homothecies and has two orbits. Jul 30 revised Homeomorphisms of X form a topological group added 92 characters in body Jul 9 awarded Nice Answer Jun 28 comment Do we have a “short five lemma” for any two of the isomorphisms? Yes,$A$and$A'$are the kernels of$B\to C$and$B'\to C'$, and the vertical map$B\to B'$maps the kernel of$B\to C$isomorphically to the kernel of$B'\to C'$. Jun 24 comment Applications of Complex Analysis. Laplace transforms are used in engineering, they produce the transfer functions of a mechanical system, whose poles and zeros and phase have physical meaning, but I doubt techniques from complex analysis is being used regularly. Jun 18 comment Looking For a Neat Proof of the Fact that the Grassmannian Manifold is Hausdorff @caffeinemachine yes indeed. Jun 12 comment Existence of diffeomorphism through convergence in Hausdorff distance It's strange indeed, as the Hausdorff distance isn't a metric on open sets, you can have open sets that are distinct and have zero Hausdorff distance... Jun 12 comment Is the sum of the following series a finite number or not? Explain.$ \sum_{k=1}^\infty \frac{5\sin^2k}{k!} $Where are you stuck, and what have you tried? Jun 12 revised Does every bijection of$\mathbb{Z}^2$extend to a homeomorphism of$\mathbb{R}^2\$? added 368 characters in body