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 …

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

May 9, 2016 · Prove that the sequence $\\{1, 11, 111, 1111, .\\ldots\\}$ will contain two numbers whose difference is a multiple of $2017$. I have been computing some of the immediate multiples of $2017$ …

@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 a …

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 ...

Oct 7, 2020 · let a and b be real numbers such that a>0 and b>1. Consider the sequence (Un) defined by U0 = a U 0 = a and Un+1 = a + 1−b−n 2.Un U n + 1 = a + 1 b n 2 U n . Show that (Un) is …

Jun 10, 2024 · Minimizing KL-divergence against un-normalized probability distribution Ask Question Asked 1 year, 7 months ago Modified 1 year, 7 months ago

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 …

I'm working on a double induction problem with the following prompt: Prove by induction on n n that for any real number q> 1 q> 1 and integer n ≥ 0 n ≥ 0:

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.