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 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. …

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...

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 is proved, for example, here and here, but I'd like to read the original work of Aubin. However, all I got is only a brief review (from MathSciNet).

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Show that $4 - Un+1 < 1/2 (4 - Un)$ Ask Question Asked 10 years, 9 months ago Modified 10 years, 9 months ago

Dec 19, 2022 · $$ \\mbox{What can we say about the integral}\\quad \\int_{0}^{a} x!\\,{\\rm d}x\\ ?. $$ Or something like $\\displaystyle\\int_{0}^{3} x!\\ {\\rm d}x\\ ?$.

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Possible Duplicate: choose a random number between 0 and 1 and record its value. and keep doing it until the sum of the numbers exceeds 1. how many tries? So I'm reading a book about simulation...

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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...