general
Why is the graph of $sec^2(x)/tan^2(x)$ continuous at $x=\pi /2$?
$f(x)=\frac{sec^2(x)}{tan^2(x)}$ Domain of $sec^2(x)$ and $tan^2(x)$ is $\mathbb{R}-(2n+1)\frac{\pi}{2}$, for $n \in \mathbb{Z}$, hence $f(x)$ also has th...
Apr 19, 2026
Archive: General
general
Are all notation equal by derivatives?
Here I read that Suppose you have a general function: y = f(x). All of the following notations can be read as "the derivative of y with respect to x" or l...
Apr 19, 2026
general
Increasing function on R that is discontinuous on the rationals
The question (Folland's Real Analysis, 3.5.30) asks to produce an increasing function on $\mathbb{R}$ whose set of discontinuities is the rationals. ...
Apr 19, 2026
general
How to prove area of the square and parallelogram the same?
Please show me how do you find length of BH or AI (in general), I want both specific proof for this case and in a general case. My purpose is to try to pr...
Apr 19, 2026
general
How many numbers are there of 5 figures..
How many numbers can be considered of five figures (from 10000 to 99999) if we require that exactly four different figures appear in nondecreasing order (...
Apr 19, 2026
general
Is there any difference between linear dependence, collinearity and coplanarity?
The way it seems to me, linearly dependent vectors have to be collinear, and collinear vectors have to be coplanar. However, since a plane doesn't re...
Apr 19, 2026
general
Origins of conjunction and disjunction symbols ($\wedge$ and $\vee$) in formal logic
I hope this question isn't off-topic: I'm just curious. In logic, we commonly use $\wedge$ and $\vee$ to represent conjunction and disjunction r...
Apr 19, 2026
general
Diagonal Matrix, just eigenvalues?
Assuming I've tested for diagonalization, can I just take the eigenvalues and arbitrarily place them in in the i,j cells to produce a diagonal matrix...
Apr 19, 2026
general
Existence of Principal Ideal
My first question is DOES a Principal Ideal always exist in a ring? (My thoughts: By it's very definition any element can generate a PI and hence it ...
Apr 19, 2026
general
Checking if a function is injective and surjective
I am doing past paper question and came across the following question: For each of the following functions, decide whether it is injective and surjective....
Apr 19, 2026
