(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 this case, the union …
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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 …
optimization - Minimizing KL-divergence against un-normalized ...
Jun 10, 2024 · Minimizing KL-divergence against un-normalized probability distribution Ask Question Asked 1 year, 5 months ago Modified 1 year, 5 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 ...
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 …
probability - If $U\sim U (-1,1)$ and $N\sim N (0,1)$ are independent ...
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.
The sequence of integers $1, 11, 111, 1111, \ldots$ have two elements ...
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 multiples of $2017$ …
probability - Suppose that $U1, U2, ..., Un$ are iid $U (0,1)$ and $Sn ...
Nov 2, 2022 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I …
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.