general
Determine if $y = x^2$ is injective
I realize that $y=x^2$ is not injective. It is not one-to-one ($1$ and $-1$ both map to 1, for example). However, in class it was stated that a function i...
Apr 21, 2026
Archive: General
general
Constant sequence?
Consider a sequence with strictly positive terms $(a_n)_{n\geq1}$ with the property: $$\lim_{n\rightarrow \infty} \left(\frac{a_1}{a_2}+\frac{a_2}{a_3} + ...
Apr 21, 2026
general
When is $\binom{n}{k}$ divisible by $n$?
Is there any way of determining if $\binom{n}{k} \equiv 0\pmod{n}$. Note that I am aware of the case when $n =p$ a prime. Other than that there does not s...
Apr 21, 2026
general
Fractional Binomial Coefficients
I recently examined the binomial coefficient $\binom{\frac{1}{2}}{k}$ and found that the denominator was always a power of two. The same is true of $\bino...
Apr 21, 2026
general
What is the Alexander polynomial of knot $6_{1}$?
My Alexander polynomial for $6_{1}$ knot is $t^4−5t^3+8t^2−5t+1$ , so its span is 4, so the lower bound of its genus is (1/2 span of its Alexander polynom...
Apr 21, 2026
![Are the square roots of all non-perfect squares irrational? [duplicate]](https://news.conceivablytech.com/uploads/are-the-square-roots-of-all-non-perfect-squares-irrational-duplicate_720.jpg)
general
Are the square roots of all non-perfect squares irrational? [duplicate]
I was asked to define a non-perfect square. Now obviously, the first definition that comes to mind is a square that has a root that is not an integer. How...
Apr 21, 2026
general
Tail Value at Risk of Normal Distribution
For a random variable $X$, Tail-value-at-risk is denoted as $\operatorname{TVaR}_p(X) = \operatorname E(X \mid X>\pi_p) = \dfrac{ \int_{\pi_p}^\infty x...
Apr 21, 2026
general
Find epipolar lines from fundamental matrix
I have two sets of 2D points and a matching between them (correspond to the same 3D points captured on two photographs). I found a fundamental matrix F. I...
Apr 21, 2026
![What number comes next in the sequence $7, 16, 8, 27, 9,...$? [closed]](https://news.conceivablytech.com/uploads/what-number-comes-next-in-the-sequence-7-16-8-27-9-closed_720.jpg)
general
What number comes next in the sequence $7, 16, 8, 27, 9,...$? [closed]
What number comes next in this series? $$7, 16, 8, 27, 9,...$$ I thought it was $38$, but I'm wrong. It is a multiple choice, and options are $27, 10...
Apr 21, 2026
general
Is basis vectors orthonormality mandatory for SVD?
I have been trying to understand intuitively the Singular Value Decomposition(SVD) and broadly speaking I tend to think of it as of a generalisation of Ei...
Apr 20, 2026
