news
What's going on with "compact implies sequentially compact"?
I've seen both counterexamples and proofs to "compact implies sequentially compact", and I'm not sure what's going on. Apparently...
Apr 17, 2026
Archive: News
news
Squaring $e^{-ax^2}$ graph
When studying wavefunctions in Chemistry, we modelled an oscillator in the form $e^{-ax^2}$. When I squared this wave function (taking $a = 1$) and plotte...
Apr 17, 2026
news
Finding the Fourier transform of shifted rect function
This is my procedure but I am unsure if I did the right thing after talking with some of my peers. $$f(x) =\mathrm{rect}\bigg|\frac{x-x_0}{a} \bigg|= \beg...
Apr 17, 2026
news
Coordinates of Fourth Vertex of Parallelogram
I have the points: $A=(1,2,0)$, $B=(-2,0,3)$, $C=(3,-4,-1)$, and I want to find the coordinate of a fourth point $D$ such that $ABCD$ is a parallelogram. ...
Apr 17, 2026
news
Notation for discrete intervals
The well-known notation for continuous intervals is $[a,b]$. But what's the case for discrete intervals? Actually they are sets of finite elements $\...
Apr 17, 2026
news
trouble finding $a$ and $r$ for geometric series formula
$\sum_{n=1}^\infty \frac1{2^n} $ Somehow this gives $a = \frac12$, $r = \frac12$ to put into the formula $\sum_{n=1}^\infty ar^{n-1}$. whats a general met...
Apr 17, 2026
news
Find the period of $2\sin(2x)\cos^2(x)$
I tried: $$2\sin(2x)\cos^2(x) = \\ 2\cdot\cos x\cdot\sqrt{\sin x(1-\sin x)(1+\sin x)} = \\ 2\cdot \sqrt{1-\sin^2x}\cdot\sqrt{\sin x (1-\sin x)(1+\sin x)} ...
Apr 17, 2026
news
A way to write decimal fractions like $1.333\dots$
Sorry if my question sounds odd; I'm a typographer, not a mathematician. Is there a better way to write decimal fractions like $1.333\dots$ or $1.444...
Apr 17, 2026
news
Find the Maximum Likelihood Estimator of $\theta$.
Let $X_1,X_2,...,X_n$ be a random sample of size $n$ from a population with density $f(x) = \left\{ \begin{array}{lr} e^{\theta-x} & , x \geq\theta\\ ...
Apr 17, 2026
news
How to come up with One-To-One and Onto Examples
I'm trying to come up with example functions that are $N \rightarrow N$ for each category: One-to-one but not onto. Onto but not one-to-one. Nether o...
Apr 17, 2026
