$x^2+y^2$, quasiconcavity and upper level set
I am having some trouble wrapping my head around quasiconcavity. I have a couple of definitions: A function $f$ defined on a convex set $S$ is quasiconcav...
Apr 21, 2026 1 VIEWS
Topic: General
5104 Articles 
How to prove a point in a set is an extreme point of the set ?
Def: an extreme point of a set $K$ is the point that cannot be expresssed as a convex combination of other points in $K$. Apart from the definition, what ...
Apr 21, 2026 1 VIEWS
a simple proof that $\pi$ is irrational by Ivan Niven
The following is Ivan Niven's simple proof that $\pi$ is rational: Here I didn't understand this part: For $0\lt x\lt \pi,$ $$0\lt f(x)\sin x\lt...
Apr 21, 2026 1 VIEWS
Examples of real places of a field K
I am studying the basic theory of valuations and places of a field $K$. The definition of a place is a homomorphism $p$ : $\mathcal{O_v} \longrightarrow K...
Apr 21, 2026 1 VIEWS
How can I find the area of the region bounded by the hyperbola
now I got region question.... The question was "find the area of the region bounded by the hyperbola $9x^{2} - 4y^{2} = 36$ and the line $x = 3$ I drew th...
Apr 21, 2026 1 VIEWS
Calculating Null T and Range T for the linear transformation $T(x,y,z)=(x+2y-z,y+z,x+y-2z)$?
I have a doubt regarding the calculation of range of a linear transformation. I will explain my doubt with an example. Suppose, $T:R^3 \to R^3 \ni$ $T(x,y...
Apr 21, 2026 1 VIEWS
Correlation between three variables question
I was asked this question regarding correlation recently, and although it seems intuitive, I still haven't worked out the answer satisfactorily. I ho...
Apr 21, 2026 1 VIEWS
What is the relationship between "recursive" or "recursively enumerable" sets and the concept of recursion?
I understand that "recursive" sets are those that can be completely decided by an algorithm, while "recursively enumerable" sets can be listed by an algor...
Apr 21, 2026 1 VIEWS
Finding the values of the real constants such that the limit exists
Find the values of the real constants $c$ and $d$ such that $$\lim_{x\to 0}\frac{\sqrt{c+dx}-\sqrt{3}}{x}=\sqrt{3}$$ I really have no clue how to even get...
Apr 21, 2026 1 VIEWS
Orthonormal system of simultaneous eigenvectors
Suppose we have a commutative family of compact, self-adjoint operators on a Hilbert space. Prove that there is an orthonormal system of simultaneous eige...
Apr 21, 2026 3 VIEWS
Can somebody explain the plate trick to me?
I learned of the plate trick via Wikipedia, which states that this is a demonstration of the fact that SU(2) double-covers SO(3). It also offers a link to...
Apr 21, 2026 1 VIEWS
Why is $\infty \cdot 0$ not clearly equal to $0$?
I did a bit of math at school and it seems like an easy one - what am I missing? $$n\times m = \underbrace{n+n+\cdots +n}_{m\text{ times}}$$ $$\quad n\tim...
Apr 20, 2026 3 VIEWS