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 …

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

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 ...

Oct 3, 2017 · Yes, that's right, and yes, $\pi_1$ should be $\mathbb {Z}$ for all $N$ in the table.

Nov 2, 2022 · I meant it to read: P (S_1 ≤ t) P (S_n ≤t). The product of those probabilities given the assumption is true.

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

@NeilsonsMilk, ah, it did not even occur to me that this involves a step. See, where I learned mathematics, it is not unusual to first define when a sequence converges to zero (and we have …

Sep 4, 2015 · Writing an expression with a variable number of terms/factors and treating it as if it were fixed formulas is a very bad idea in doing differentation. You will find examples under the …