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(Un-)Countable union of open sets - Mathematics Stack Exchange
$\begingroup$ 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.
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 Product R...
Intuitive proof that $U(n)$ isn't isomorphic to $SU(n) \\times S^1$
Jan 5, 2016 · This is a sort of addendum to Qiaochu's answer, the purpose of which is to tie up the loose end it leaves in the sense that it only considers isomorphisms compatible with the short exact sequence associated to the surjective $\det\colon \mathrm{U}(n) \to S^1$.
Calculate the cohomology group of $U(n)$ by spectral sequence.
May 31, 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Equation of a rectangle - Mathematics Stack Exchange
Oct 2, 2011 · For purposes of plotting with a computer, the implicit equation isn't terribly convenient to handle, so I'll throw in a set of parametric Cartesian equations for free, based on the parametric equations of the Lamé curve:
Lie Algebra of U (N) and SO (N) - Mathematics Stack Exchange
U(N) and SO(N) are quite important groups in physics. I thought I would find this with an easy google search. Apparently NOT! What is the Lie algebra and Lie bracket of the two groups?
$U(n) \\simeq \\frac{SU(n) \\times U(1)}{\\mathbb{Z}_{n}}
Jan 20, 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Can an underdetermined system have a unique solution?
Oct 5, 2012 · In my case, I am calling an underdetermined system as a system of linear equations where there are fewer equations than variables (unknowns). My textbook says the answer is false, however the inter...
How do we calculate factorials for numbers with decimal places?
I was playing with my calculator when I tried $1.5!$. It came out to be $1.32934038817$. Now my question is that isn't factorial for natural numbers only? Like $2!$ is $2\\times1$, but how do we e...
Proving that a convergent sequence has a unique limit
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