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 Dec 18 answered Let $X=\left\{f\in\mathbb{N}^\mathbb{N} : \;|f(n + 1)-f(n)|=1\right\}$. Prove that cardinality of $X$ is continuum. Dec 17 answered Conxex combinations of max and min Dec 16 reviewed Approve How to show path-connectedness of $GL(n,\mathbb{C})$ Dec 16 reviewed Reject Express the indefinite integral $\int\sin x^2~dx$ as a power series Dec 15 comment If $f(x)$ is differentiable on $(a,b)$, is $f(x)$ continuous on $[a,b]$? And even if $f$ is defined on $[a,b]$, $f$ needn't be continuous there, e. g. $$x \mapsto \begin{cases} \sin x^{-1} & x > 0\\ 0 & x = 0 \end{cases}$$ Dec 15 comment Is Wolfram Alpha wrong with a simple derivative? Just add a * to tell wolfram you want multiplication, not application ... and everything works as expected: wolframalpha.com/input/?i=d[%28x^2w*%28y-z%29t%29%2F%2818l%29%2Cw] Dec 13 comment Improper Multivariable Integrals The second integral converges at infty (in the Lebesgue sense) if the exponent or $r$ is less then $-1$, as the sine is bounded ... Dec 13 revised Find the series expansion of $f(z)=\frac{4}{(z-1)(z+3)}$ around $z_0=-1$. fixed title Dec 13 answered How to calculate a matrix with its orthogonal complement known? Dec 12 revised Prove the following trigonometric identity. TeXification Dec 12 reviewed Approve Prove the following trigonometric identity. Dec 12 revised boundary conditions after change of variables TeXification Dec 12 comment Is there an Artinian ring with exactly two prime ideals which their product is non-zero? Thanks ... it was to easy ... Dec 11 comment Improper Multivariable Integrals No, it represents (if you want to say it like that) $n-1$ 1-dimensional integrals, as a sphere is a $n-1$-dimensional object. I wanted to mark that we integrate with respect to the surface measure of the sphere. Dec 11 comment Prove or disprove matrix $A$ and $A^T$ is Matrix congruence? $A$ and $A^t$ are similar: math.stackexchange.com/questions/62497/… Dec 11 comment Radius of convergence of a power series. Note that your attempt only shows that $\limsup a_n^{1/n} \le 1$, that is $R \ge 1$. To prove that $R=1$ you have to prove that also $\limsup a_n^{1/n} \ge 1$, that is find a sequence of $n$s with $a_n^{1/n} \to 1$ Dec 11 comment matrix method for solving system of linear equations @MarcvanLeeuwen Thanks ... Dec 11 answered Entropy Solution of the Burger's Equation Dec 10 comment maximal subgroup of a group $M$ being maximal only gives you $N_G(M) = M$ or $N_G(M) = G$. Dec 10 comment Improper Multivariable Integrals (1) Yes, $rS^{n-1} = \{rx \mid x \in S^{n-1}$. And by writing $dS(x)$ I tried to make explicit that the variable with respect to which we integrate is $x$.