- (Un-)Countable union of open sets - Mathematics Stack Exchange
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 In other words, induction helps you prove a
- Newest Questions - Mathematics Stack Exchange
Mathematics Stack Exchange is a platform for asking and answering questions on mathematics at all levels
- modular arithmetic - Prove that that $U (n)$ is an abelian group . . .
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
- For what $n$ is $U_n$ cyclic? - Mathematics Stack Exchange
17 Un U n is cyclic iff n n is 2 2, 4 4, pk p k, or 2pk 2 p k, where p p is an odd prime The proof follows from the Chinese Remainder Theorem for rings and the fact that Cm ×Cn C m × C n is cyclic iff (m,n)= 1 (m, n) = 1 (here Cn C n is the cyclic group of order n n)
- probability - Suppose that $U1, U2, . . . , Un$ are iid $U (0,1)$ and $Sn . . .
I meant it to read: P (S_1 ≤ t) P (S_n ≤t) The product of those probabilities given the assumption is true
- Double induction example: $ 1 + q + q^2 + q^3 + \cdots + q^ {n-1} + q^n . . .
Slightly relevant: you can see my answer on this thread for a proof that uses double induction (just to get you exposed to how the mechanics of a proof using double induction might work)
- The sequence of integers $1, 11, 111, 1111, \ldots$ have two elements . . .
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 $2017$ to see how
- Mnemonic for Integration by Parts formula? - Mathematics Stack Exchange
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
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