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 …

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 …

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 ...

(If you know about ring theory.) Since $\mathbb Z_n$ is an abelian group, we can consider its endomorphism ring (where addition is component-wise and multiplication is given by …

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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 …

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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 ...

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