general
why don't we define vector multiplication component-wise?
I was just wondering why we don't ever define multiplication of vectors as individual component multiplication. That is, why doesn't anybody eve...
Apr 10, 2026
Archive: General
general
Arcsine law for Brownian motion
Here is the question: $(B_t,t\ge 0)$ is a standard brwonian motion, starting at $0$. $S_t=\sup_{0\le s\le t} B_s$. $T=\inf\{t\ge 0: B_t=S_1\}$. Show that ...
Apr 10, 2026
general
What is the difference between the relations $\in$ and $\subseteq$?
What is the difference between the relations "$\in$" and "$\subseteq$" ? Don't they both mean that something is an element of a set? Are they interch...
Apr 10, 2026
general
Definition of Global Convergence
I am confused by the notion of "global convergence" as used in numerical optimization literature, and did not find an exact definition for that yet. Now I...
Apr 10, 2026
general
What is negation?
I asked this question, caused by a confusion that I was able to crystallize in the comment section of ryang's answer. What is negation? One could def...
Apr 10, 2026
general
Complex exponential $e^z$ graph
Sketch the following regions: $\operatorname{Arg}(e^z)>\dfrac{π}{4}$ ${e^z|\operatorname{Im}(z) = 1}$ $|e^z| > 2$ I am confused of graphing $e^z$ fu...
Apr 10, 2026
general
Given roots (real and complex), find the polynomial
This is not a duplicate of theory of equations finding roots from given polynomial. Given that the roots (both real and complex) of a polynomial are $\fra...
Apr 10, 2026
general
$P(x)$ consists of the integers -2, -1, 0, 1 and 2. Write out each of these propositions using disjunctions, conjunctions and negations.
Suppose that the domain of the propositional function $P(x)$ consists of the integers -2, -1, 0, 1 and 2. Write out each of these propositions using disju...
Apr 10, 2026
general
Where can I find the Inscribed Rectangle Problem proof?
I've been looking into the Toeplitz' Conjecture and became very interested, so I began to study it. Here is the conjecture: For any Jordan curve...
Apr 10, 2026
general
Fourier transform of generalized function $\frac{1}{|x|^2-1+i0}$ on $ \mathbb{R}^3$
I am looking for an explicit computation of (or a reference to) the Fourier transform of the generalized function on $\mathbb{R}^3$ $$\frac{1}{|x|^2-1+i0}...
Apr 10, 2026
