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 …

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 ...

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 …

2 days ago · Mathematics Stack Exchange is a platform for asking and answering questions on mathematics at all levels.

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

Aug 3, 2023 · (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 …

Nov 2, 2022 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation …