general
Calculate $\pi$ precisely using integrals?
This is probably a very stupid question, but I just learned about integrals so I was wondering what happens if we calculate the integral of $\sqrt{1 - x^2...
Apr 15, 2026
Archive: General
general
Locations of root theorem confusion
Theorem: if f is continuous in [a, b] and f(a) < 0, f(b) > 0, then there exists c in [a, b] such that f(c) = 0. The most popular proof on the website i...
Apr 15, 2026
general
Schur decomposition
If $A$ is real and nonsymmetric with Schur decomposition $UTU^H$, then what types of matrices are $U$ and $T$? How are the eigenvalues of $A$ related to $...
Apr 15, 2026
![Why is absolute value function not a polynomial? [closed]](https://news.conceivablytech.com/uploads/why-is-absolute-value-function-not-a-polynomial-closed_720.jpg)
general
Why is absolute value function not a polynomial? [closed]
Why is absolute value function not a polynomial? I need a clear answer to this question please,? Why couldn't we consider absolute value function as ...
Apr 15, 2026
general
How can we show that at least one of the triangles $PAB,PBC,PAC$ has a smaller perimeter than $ABC$?
For any triangle $ABC$ on the plane, we draw a circle $\Omega$ with center $O$ such that $AB$ is its diameter. We place a point $P$ inside $\Omega$. How c...
Apr 15, 2026
general
The fundamental theorem of Galois theory
Let $E/Q$ be a Galois extension of degree $p^2$, where $p$ is a prime number. Prove that $L/Q$ is a Galois extension for any $L \in Intermediate(E/Q)$ and...
Apr 15, 2026
general
Do Symmetric Games with Nash Equilibria always have a symmetric Equilbrium?
Define a game with S players to be Symmetric if all players have the same set of options and the payoff of a player depends only on the player's choi...
Apr 15, 2026
general
How many strings of four decimal digits that do not contain the same digit three times?
Hello, everyone! I received the following question as part of my Discrete Mathematics course and am unable to solve it. How many strings of four decimal d...
Apr 15, 2026
general
What exactly is infinity?
On Wolfram|Alpha, I was bored and asked for $\frac{\infty}{\infty}$ and the result was (indeterminate). Another two that give the same result are $\infty ...
Apr 15, 2026
general
Rules of Double Sums
Wat are the (most important) rules of double sums? Below are some rules I encountered - are they all correct and complete? Offerings of clear intuition or...
Apr 15, 2026
