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- (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 of any finite collection of open sets is open) the validity of the property for an infinite collection doesn't follow from that In other words, induction helps you prove a
- Mnemonic for Integration by Parts formula? - Mathematics Stack Exchange
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 Product R
- 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
- optimization - Minimizing KL-divergence against un-normalized . . .
Minimizing KL-divergence against un-normalized probability distribution Ask Question Asked 1 year, 4 months ago Modified 1 year, 4 months ago
- For what $n$ is $U_n$ cyclic? - Mathematics Stack Exchange
Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges,
- Newest Questions - Mathematics Stack Exchange
Mathematics Stack Exchange is a platform for asking and answering questions on mathematics at all levels
- Homotopy groups U(N) and SU(N): $\\pi_m(U(N))=\\pi_m(SU(N))$
Yes, that's right, and yes, $\pi_1$ should be $\mathbb {Z}$ for all $N$ in the table
- Intuitive proof that $U(n)$ isnt isomorphic to $SU(n) \\times S^1$
The "larger" was because there are multiple obvious copies of $U (n)$ in $SU (n) \times S^1$ I haven't been able to get anywhere with that intuition though, so it
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