While digging through some dusty corners of my file cabinet, I found a photocopied sheet of eight (handwritten) problems from 1985 that I recall receiving from my secondary school mathematics teacher way back when. Four of the problems are labeled “Set U” and the other four are labeled “Set V”. I’m reproducing “Set U” below, … Read more
Consider a poset $(X, \geq)$. Let’s define a new relation $\succsim$ on subsets of $X$: for $A, B\subseteq X$, say $A\succsim B$ if for any $a\in A$ and any $b\in B$, we have $a\geq b$. Does such a relation already have a name? Note that the relation is not a preorder (reflexivity fails). Answer AttributionSource … Read more
This question was inspired by Can we build a continuous function from “fibers”/preimages defined over a topological base? Let $X,Y$ be sets and $L\subseteq \mathcal{P}(Y)$. Suppose $L$ has the following properties: $\emptyset, Y\in L$; $L$ is closed under arbitrary unions and intersections. Let $F: L\to \mathcal{P}(X)$ be a function such that $F(\emptyset) = \emptyset$ and … Read more
Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for MathOverflow. Closed 8 years ago. Improve this question I guess most of us didn’t meet Polya in person (this is the answer to the title)! Perhaps, it is much easier to guess … Read more
It’s difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center. Closed 11 years ago. Background I’m interested in the issue of “explanatory” … Read more
My son has been working on equations for finding length of the length of a curve without any resources (computers, calculators…) while in prison. He is wondering if he is on the right path. Sadly my understanding of mathematics is severely limited; I cannot help him. Dear mathematicians, could you please offer him some feedback? … Read more
I know of a few applications of De-Bruijn Sequences and De Bruijn Graphs in combinatorics, applied mathematics, Engineering and computer science. But I have only found one application of De Bruijn sequences in “pure mathematics”, specifically in Diophantine approximations, which is the following: http://eprints.whiterose.ac.uk/126995/1/160507953v3.pdf Do you know of any other such applications of De Bruijn … Read more
This largest solution to this gorgeous equation is the first local extremum on a function related to the Fibonacci sequence: $$x^2 \cdot \sin \left(\frac{2\pi}{x+1} \right) \cdot \left(3+2 \cos \left(\frac{2\pi}{x} \right) \right) = (x+1)^2 \cdot \sin \left(\frac{2\pi}{x} \right) \cdot \left(3+2 \cos \left(\frac{2\pi}{x+1} \right) \right)$$ This is as simplified as I could get it. The largest solution … Read more
Mobius transformations map circles to circles. Wiki says ‘Möbius transformations can be more generally defined in spaces of dimension n>2 as the bijective conformal orientation-preserving maps from the n-sphere to the n-sphere’. Is there an explicit way to given such transformations in n-dimenstions? Answer Yes, and, indeed, these examples special cases of the situation that … Read more
I am not sure whether this was asked before, but I didn’t find a reference in GAP system documentation on how to print the history of the command line (Ubuntu installation). For instance: gap> G := Group((1,2)(3,4),(1,2,3)); > irr := Irr(G); How to save or print the list of my previous commands (similar to history … Read more
