# Tagged Questions

For questions concerning a specific proof, asking for verification, identifying errors, suggestions for improvement, etc.

48 views

### What is the best time complexity of checking the inequality $a_1x_1 + \cdots + a_mx_m \le K$ to have a non-negative integer solution?

Consider $$a_1x_1 + \cdots + a_mx_m \le K$$ with $a_1, a_2, \ldots , a_m$ and $K$ being integers. I only need to know if the inequality has an integer solution or not. It means that there is ...
41 views

### Help with proof that $E(G|a < G < b) \lt E(H|a < H < b)$ for truncated normal distributions

Consider two independent normally distributed random variables with equal standard deviations, $G\sim N (\mu_{G}, \sigma)$ and $H\sim N (\mu_{H}, \sigma)$ that are truncated between points $a$ and $b$....
27 views

27 views

21 views

32 views

### The Greatest Number of Edges on a Bipartite Graph

Let $G$ be a bipartite graph on $p$ vertices. Find a formula in terms of $p$ that determines the greatest number of edges that $G$ could have. Prove that this formula is correct. Let $V$ be the set ...
53 views

28 views

### Is it possible for two triangles to be different if the sides of one is equal to another?

I was reading Euclid's Elements E-book I found online and got stuck on this concept. I will just copy what I found to be very absurd. There could still be another different triangle with the same ...
210 views

19 views

24 views

### Applying topological definition of continuity to $f(x) = \frac{1}{x}$

I am trying to show that the function $f:\mathbb{R} \rightarrow \mathbb{R}$ defined by $$f(x) = \left\{ \begin{array}{l} \frac{1}{x}, \, x > 0 \\ 0, \, x \leq 0 \end{array} \right.$$ is not ...
32 views

36 views

36 views

### Minimal perimeter of a triangle

Imagine a triangle with a base $[0, s]$ and a height $h$. ($s, h \gt 0$) For what orthocentre $x$ does the triangle have a minimal perimeter and how long is it? Now, the proof starts with: ...
### A clean proof of $x^2 \geq x$, for any integer $x$
I am trying to prove that $x^2 \geq x$ for any integer $x$. Since we know that for any number $n$, $n^2 \geq 0$ we conclude that if $x \leq 0$ the proposition will hold. Next we must prove that the ...