(Un-)Countable union of open sets - Mathematics Stack Exchange
Jun 4, 2012 · 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 …
Newest Questions - Mathematics Stack Exchange
1 day ago · Mathematics Stack Exchange is a platform for asking and answering questions on mathematics at all levels.
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 …
The sequence of integers $1, 11, 111, 1111, \ldots$ have two …
May 9, 2016 · Prove that the sequence $\ {1, 11, 111, 1111, .\ldots\}$ will contain two numbers whose difference is a multiple of $2017$. I have been computing some of the immediate …
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 …
optimization - Minimizing KL-divergence against un-normalized ...
Jun 10, 2024 · Minimizing KL-divergence against un-normalized probability distribution Ask Question Asked 1 year, 6 months ago Modified 1 year, 6 months ago
modular arithmetic - Prove that that $U (n)$ is an abelian group ...
Prove that that $U(n)$, which is the set of all numbers relatively prime to $n$ that are greater than or equal to one or less than or equal to $n-1$ is an Abelian ...
probability - If $U\sim U (-1,1)$ and $N\sim N (0,1)$ are …
Apr 15, 2023 · If $U$ and $N$ are independent r.v.'s (with finite moments of order $4$) then $U$ and $UN$ CANNOT be independent unless $U$ is a constant.
$U(n) \\simeq \\frac{SU(n) \\times U(1)}{\\mathbb{Z}_{n}}
Jan 20, 2015 · I'm trying to proof the following isomorphism $$U (n) \simeq \frac {SU (n) \times U (1)} {\mathbb {Z}_ {n}}$$ So I'm using the first Isomorphism theorem: http://en ...
Generation of Hermite polynomials with Gram-Schmidt procedure
Feb 8, 2019 · Hello reader! I have missed factor in the denominator of H_0 (x) while calculating H'_1 (x), one must divide it by normalisation of H_0 (x). And same goes for every use of H_n …