(Un-)Countable union of open sets - Mathematics Stack Exchange
A remark: regardless of whether it is true that an infinite union or intersection of open sets is open, when you have a property that holds for every finite collection of sets (in this case, the union or …
modular arithmetic - Prove that that $U (n)$ is an abelian group ...
Prove that that U(n) U (n), which is the set of all numbers relatively prime to n n that are greater than or equal to one or less than or equal to n − 1 n 1 is an Abelian group. My thought …
For what $n$ is $U_n$ cyclic? - Mathematics Stack Exchange
When can we say a multiplicative group of integers modulo $n$, i.e., $U_n$ is cyclic? $$U_n=\\{a \\in\\mathbb Z_n \\mid \\gcd(a,n)=1 \\}$$ I searched the internet but ...
Newest Questions - Mathematics Stack Exchange
1 day ago · Mathematics Stack Exchange is a platform for asking and answering questions on mathematics at all levels.
Mnemonic for Integration by Parts formula? - Mathematics Stack …
Nov 11, 2018 · The Integration by Parts formula may be stated as: $$\\int uv' = uv - \\int u'v.$$ I wonder if anyone has a clever mnemonic for the above formula. What I often do is to derive it …
Carleman Estimates - Mathematics Stack Exchange
I'm looking for the article Carleman, T. Sur un problème d'unicité pur les systèmes d'équations aux dérivées partielles à deux variables indépendantes. (French) Ark. Mat., Astr. Fys. 26, …
$\\operatorname{Aut}(\\mathbb Z_n)$ is isomorphic to $U_n$.
Aug 3, 2023 · It might be using ring theory in a non-essential way, but it is conceptually simpler because the endomorphisms are easier to describe than the automorphisms, and since the …
If a series converges, then the sequence of terms converges to $0$.
@NeilsonsMilk, ah, it did not even occur to me that this involves a step. See, where I learned mathematics, it is not unusual to first define when a sequence converges to zero (and we have …
Intuitive proof that $U(n)$ isn't isomorphic to $SU(n) \\times S^1$
Jan 5, 2016 · The "larger" was because there are multiple obvious copies of $U (n)$ in $SU (n) \times S^1$. I haven't been able to get anywhere with that intuition though, so it ...
probability - Suppose that $U1, U2, ..., Un$ are iid $U (0,1)$ and …
Nov 2, 2022 · I meant it to read: P (S_1 ≤ t) P (S_n ≤t). The product of those probabilities given the assumption is true.