(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 intersection …
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 process: for a, b ∈ …
Newest Questions - Mathematics Stack Exchange
Mathematics Stack Exchange is a platform for asking and answering questions on mathematics at all levels.
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, (1939). ...
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 ...
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 from the …
$\\operatorname{Aut}(\\mathbb Z_n)$ 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 invertible …
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 a …
Homotopy groups U(N) and SU(N): $\\pi_m(U(N))=\\pi_m(SU(N))$
Oct 3, 2017 · Yes, that's right, and yes, $\pi_1$ should be $\mathbb {Z}$ for all $N$ in the table.
When is the group of units in $\\mathbb{Z}_n$ cyclic?
Let Un U n denote the group of units in Zn Z n with multiplication modulo n n. It is easy to show that this is a group. My question is how to characterize the n n for which it is cyclic. Since the multiplicative …