(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
3 days ago · Mathematics Stack Exchange is a platform for asking and answering questions on mathematics at all levels.
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 ...
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 …
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.
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
functional analysis - Where can I find the paper "Un théorème de ...
Nov 12, 2015 · J. P. Aubin, Un théorème de compacité, C.R. Acad. Sc. Paris, 256 (1963), pp. 5042–5044. It seems this paper is the origin of the "famous" Aubin–Lions lemma. This lemma …
Show that $\left (1+\dfrac {1} {n}\right)^n$ is monotonically …
Jul 7, 2012 · We use the inequality between the geometric mean and the arithmetic mean for the following positive numbers $$ x_ {1}=1,~x_ {2}=x_ {3}=\ldots=x_ {n+1}=1+\frac {1} {n ...
"Unramified" extensions of a $p$-adic field with prescribed ...
Jul 24, 2025 · When taking the completion, you exclusively add transcendental elements (indeed, elements of $\overline {\mathbb Q_p} \setminus E^ {un}$ are ramified over $\Bbb Q_p$ which …