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 Apr17 comment Show that the set of isolated points of $S$ is countable Look at Theorem 4 in here Mar28 comment Basic problem about measurable sets I misread your question Mar21 comment Is continuous and integrable function bounded? It's bounded almost everywhere. Mar12 comment Let $A^{774}=0$. Show that if $t$ is an eigenvalue of $A$, then $t=0$ Hint: minimal polynomial. Mar8 comment Show that a finite group with certain automorphism is abelian Thanks to @Vignesh Manoharan for adding the source. Mar3 comment Group theory, quotient groups? Part of the question is answered here. For the rest, hint: first isomorphism theorem. Mar1 comment What do Algebra and Calculus mean? @Tim I once heard that analysis is deduce things from the properties of the real numbers. That seemed accurate to me because everywhere in analysis one keep coming back to real numbers. Beautiful answer André. Mar1 comment What do Algebra and Calculus mean? @gary Algebra is more than that. Your second definition applies to whatever. Jan4 comment If every vector is an eigenvector, the operator must be a scalar multiple of the identity operator? Related Dec29 comment Prove $A=\{x\in \mathbb{R}|f(x)=x\}$ is closed subset of $\mathbb{R}$ Sequentially closedness. Dec12 comment On the problem of polynomial bijection from $\mathbb Q\times\mathbb Q$ to $\mathbb Q$ What this seems like is material worth a blogpost. Dec11 comment Relevant Dec10 comment If $\sigma$ is a cycle of length $r$, then it has order $r$? @darijgrinberg Would you like to put your comment as an answer. I'll upvote it. Dec10 comment @PedroTamaroff I don't chat as often as I used to, the few times I've been there recently, I found some things that made me form some opinion. For what is worth, I remember I used to appreciate being in chat when you were around. More, when the talk was about math. Just to make clear that I'm not trying to screw you on this elections. Dec9 comment The good thing about being active in chat is that many people gets to know you. This kind of behavior seems pretty much in opposite direction to lead by example and being patient and fair, not to talk about respect. Nov16 comment what is the set $\mathbb R[X]$ defined as? Nice answer. Multiplication can also be defined the same way for the formal power series, so multiplication of polynomials can be realized as the restriction of that one. Nov12 comment If $f(x)\ge g(x)$, is $f'(x)\ge g'(x)$? Fortunately it holds that if $f\geq g$ then $\int f\geq \int g$ with some conditions on $f$ and $g$ and several flavors of $\int$. Nov12 comment Prove $\sum_{n=1}^{\infty} n \mu(A_n) = \sum_{n=1}^{\infty}\mu(B_n) = \sum_{n=1}^{\infty} \mu(E_n)$ Yes, the triple equality doesn't holds in general. I misread the thing, wanted that can to be some other can't. Thank you for the clarification. Nov12 comment Prove $\sum_{n=1}^{\infty} n \mu(A_n) = \sum_{n=1}^{\infty}\mu(B_n) = \sum_{n=1}^{\infty} \mu(E_n)$ @DanielFischer I think you mean: "but it can't be that..." at the end of the integrals solution. Nov11 comment what is the cardinality of a Null set? What kind of null set?