Top new questions this week:
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Let's consider the following variant of Collatz $(3n+1) : $
If $n$ is odd then $n \to n^2-1.$
$1\to 0.$
$3\to 8\to 1\to 0.$
$5\to 24\to 3\to 0.$
$7\to 48\to 3\to 0.$
$9\to 80\to 5\to 0.$
$11\to 120\to ...
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EDIT: I forgot how open number theory is! (I think that gets me put on mathematician probation or something.) For this question, I will accept any answer which assumes "standard conjectures" ...
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When teaching functions in polar coordinates, the nearly universal practice is to consider functions of the form $r = f(\theta)$. I think I have never seen any examples in which $\theta$ is expressed ...
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Are these equations properly defined differential equations?
Modifications were made to a deleted question to re-focus it
Intro
Recently, in this answer I figure out that the following autonomous ...
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Suppose a coupon collector is collecting a set of $n$ coupons that he receives one-by-one uniformly at random.
If the collector stops exactly when the collection is complete, we know the expected ...
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The problem is:
Assume that $(X,\mathcal{A} , μ)$ is a finite measure space (i.e., $μ(X) < \infty $ ) and the sequence of sets $E_{j}\in \mathcal{A}$ satisfies $\sum^\infty_{j=1} μ(E_{j} )=\infty$....
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I am learning convex analysis on my own and I would appreciate some help.
I know that convex conjugate is the generalization of the Legendre transform. I also know the formula known for Legendre ...
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Greatest hits from previous weeks:
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This is a very simple but confusing puzzle.
A customer buys goods worth $200$ rupees from a shop. The shopkeeper selling these goods makes zero profit from this purchase.
The lady gives him a $1000$ ...
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My attempt to solve this problem is:
First digit cannot be zero, so the number of choices only $6 (1,2,3,4,5,6)$
The last digit can be pick from $0,2,4,6$, so the number of choices only 4
Second ...
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I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows.
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I understand intuitively that this is true, but I'm embarrassed to say I'm having a hard time constructing a rigorous proof that $|a+b| \leq |a|+|b|$. Any help would be appreciated :)
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I hear people refer to the dimensions of things as "$2$ by $4$" etc. and I know its length by width, but I can't tell if the length dimension is vertical (up and down) or horizontal (side to side). ...
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I have two square matrices: $A$ and $B$. $A^{-1}$ is known and I want to calculate $(A+B)^{-1}$. Are there theorems that help with calculating the inverse of the sum of matrices? In general case $B^{-...
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In my math lectures, we talked about the Gram-Determinant where a matrix times its transpose are multiplied together.
Is $A A^\mathrm T$ something special for any matrix $A$?
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Can you answer these questions?
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Given a binary string s of length $n>2$.An edit operation is a single character insert, delete or substitution. The edit distance between two strings is the minimum number of edit operations needed ...
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I'm studying harmonic analysis, and I'm trying to understand the fact that
$$\phi: \mathbb{R}\to \widehat{\mathbb{R}}: s \mapsto (t \mapsto \exp(2\pi i st))$$
is an isomorphism of topological groups (...
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Problem
How many ways are there to arrange $3$ men, $3$ women, $3$ children in a circle such that they alternate clockwise in this order: man, woman, child? The seats are not numbered.
My Opinion
I ...
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