general
Graph of $\sqrt x+\sqrt y=1$
The area (in sq. units) of the region bounded by the curve $\sqrt x+\sqrt y=1,x,y\ge0$, and the tangent to it at the point $(\frac14,\frac14)$ is : $\frac...
Apr 12, 2026
Archive: General
general
what is the cardinality of a Null set?
Does the cardinality of a Null set is same as the cardinality of a set containing single element? If a set A contains Null set as its subset, then the nul...
Apr 12, 2026
general
Find number of elements of order $p$ in group $G$ where $p$ is prime and $G$ has $m$ subgroups of order $p%
Find the number of elements of order $p$ in group $G$, where $p$ is prime and $G$ has $m$ subgroups of order $p$. Suppose G is a group, and p is prime. Th...
Apr 12, 2026
general
What's the terminology for whether a number is positive or negative?
Is there a word for the quality of a number to be either positive or negative? Consider this question: What's the ... (sign/positivity/negativity, bu...
Apr 12, 2026
general
Limit for $e$ and $\frac{1}{e}$
My question concerns the derivation of this: $$e^r = \lim_{n \rightarrow \infty} \left(1 + \frac{r}{n}\right)^n \ \ ...(1).$$ One of the definitions of $e...
Apr 12, 2026
![Spider-Man: No Way Home and Archimedean spiral. POSSIBLE SPOILERS [closed]](https://news.conceivablytech.com/uploads/spider-man-no-way-home-and-archimedean-spiral-possible-spoilers-closed_720.jpg)
general
Spider-Man: No Way Home and Archimedean spiral. POSSIBLE SPOILERS [closed]
In the movie while Spider-Man fights Strange it is mentioned that the dimension he is in is an Archimedean spiral, Spider-Man says "Square the radius...
Apr 12, 2026
general
A normal matrix with real eigenvalues is Hermitian
$A$ is a normal matrix (i.e. $AA^*=A^*A$, where * denotes the hermitian conjugate). If all its eigenvalues are real, prove that it is Hermitian (i.e. $A^*...
Apr 12, 2026
general
Solve for $x$ in $x^2-5x+2\sqrt{x^2-5x+3}= 12$
Solve for $x$ in $x^2-5x+2\sqrt{x^2-5x+3}= 12$ I've tried moving root term to one side and squaring both sides to get a $4$th-degree polynomial and f...
Apr 12, 2026
general
Do prime numbers have prime factors?
(This is a somewhat trivial question). Do prime numbers have prime factors, i.e. itself? For example is 7 a prime factor of 7? The reason I ask this is be...
Apr 12, 2026
general
Double orthogonal complement is equal to topological closure
So I'm in an advanced Linear Algebra class and we just moved into Hilbert spaces and such, and I'm struggling with this question. Let $A$ be a n...
Apr 12, 2026
