general
Set theoretic definition of cartesian product of two sets
I am trying to study mathematics rigorously.It is mentioned in my book in the chapter of set theory that the symbol "$:$" stands for the phrase "such that...
Apr 21, 2026
Archive: General
general
List of hyperbolic geometry models
When I studied (as an amator) non-euclidean geometry I read that big number of models of hyperbolic geometry was created in 19th and 20th century. Where c...
Apr 21, 2026
general
Convergence of a series 1/(2n+1)
I'm looking for a way to get an estimate on a sum of the following series: $$\sum_{i=1}^{n} \frac{1}{2i-1}$$ My exact question would be the solution ...
Apr 21, 2026
general
Solving an equation with trigonometric and exponential functions
While tutoring about integration and derivatives of functions, we needed to determine what the biggest distance between two functions, one trigonometric $...
Apr 21, 2026
general
How do I solve a non-homogeneous recurrence relation with constant coefficients WITHOUT the initial conditions?
I have these two recurrence relations: (i) $$a_n = 6a_{n-1} - 12a_{n-2} + 8a_{n-3} +n2^n$$ (ii) $$a_n = 6a_{n-1} - 12a_{n-2} + 8a_{n-3} +n^22^n$$ I don�...
Apr 21, 2026
general
Find the matrix of $f:(x,y,z) \rightarrow (y+z,x-y, -x+y+2z)$ in a new basis
Let $f: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ such that $$(x,y,z) \mapsto (y+z,x-z,-x+y+2z) $$ Find its matrix, then show that this function is a project...
Apr 21, 2026
![Complex numbers as exponents [duplicate]](https://news.conceivablytech.com/uploads/complex-numbers-as-exponents-duplicate_720.jpg)
general
Complex numbers as exponents [duplicate]
Is there any formula to calculate $2^i$ for example? What about $x^z$? I was surfing through different pages and I couldn't seem to find a formula li...
Apr 21, 2026
general
What's the limit of $\tan x$ when $x$ aproaches $\pi /2$ by the left?
To be more specific: $$\lim_{x\to (\pi/2)^-} \tan x$$ Thanks :)
Apr 21, 2026
general
Proof that the cross product is not associative without using components
I need to show that the cross product is not associative without using components. I understand how to do it with components, which leads to an immediate ...
Apr 21, 2026
general
How does FFT work?
For five years I tried to understand how Fourier transform works. Read a lot of articles, but nobody could explain it in simple terms. Two weeks ago I stu...
Apr 21, 2026
