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 …

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Jun 10, 2024 · Minimizing KL-divergence against un-normalized probability distribution Ask Question Asked 1 year, 4 months ago Modified 1 year, 4 months ago

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 …

Oct 7, 2020 · Show that (Un) is bounded, convergent and find its limit. To prove that the sequence is bounded i intuitively used the fixed point theorem because at first glance i don't really know …

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 …

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 ...

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.

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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 ...