Intereting Posts

Universal property of tensor products / Categorial expression of bilinearity
Working with binomial coefficient $\sum_{k=0}^n (-1)^k \binom nk=0$
How to prove that a connected graph with $|V| -1= |E|$ is a tree?
Group algebra ever a field?
Euler-Lagrange equations of the Lagrangian related to Maxwell's equations
Show that $\sqrt{2+\sqrt{2+\sqrt{2…}}}$ converges to 2
How many ways to arrange the flags?
Triangle problem – finding the angle
The Radon-Nikodym derivative of a measure such that $|\int f'\,d\mu|\le \|f\|_{L^2}$ for $f\in C^1$
Express $x^8-x$ as a product of irreducibles in $\Bbb Z_2$
Area enclosed by an equipotential curve for an electric dipole on the plane
If a linear functional is not bounded, then it has a non-closed kernel.
Maximum of $\frac{\phi(i)}i$
Consecutive birthdays probability
Find the limit of $(\sin \frac{1}{n} \cdot \sin \frac{2}{n} \cdot … \cdot \sin 1)^{\frac{1}{n}}$

Is there any rule for powers so that i can compare which one is greater without actually calculating? For example

```
54^53 and 53^54
23^26 and 26^23
3^4 and 4^3 (very simple but how without actually calculating)
```

- How is it, that $\sqrt{x^2}$ is not $ x$, but $|x|$?
- John keeps rolling a standard six-sided dice until it comes up as a 6. What is the expected number of dice rolls?
- Is there a log-space algorithm for divisibility?
- Prove that $(n!)!$ divisible by $(n!)^{(n-1)!}$
- what operation repeated $n$ times results in the addition operator?
- What is mathematical basis for the percent symbol (%)?
- How to explain that division by $0$ yields infinity to a 2nd grader
- Proof of the standard algorithm for addition?
- Simplify : $( \sqrt 5 + \sqrt6 + \sqrt7)(− \sqrt5 + \sqrt6 + \sqrt7)(\sqrt5 − \sqrt6 + \sqrt7)(\sqrt5 + \sqrt6 − \sqrt7) $
- How to compute a lot of digits of $\sqrt{2}$ manually and quickly?

If $a\gt b\gt e , b^a\gt a^b$. To see this, take logs. You want to compare $a \ln b$ with $b \ln a$. $\ln$ rises slowly, so the larger multiplier wins.

- How to find the integral $\int \tan (5x) \tan (3x) \tan(2x) \ dx $?
- A method of finding the eigenvector that I don't fully understand
- Value of $u(0)$ of the Dirichlet problem for the Poisson equation
- If a commutative ring is semiprime and its prime ideals are maximal then it is von Neumann regular (absolutely flat).
- Gamma Distribution out of sum of exponential random variables
- Equilateral Triangle Problem With Trig
- Prove “casting out nines” of an integer is equivalent to that integer modulo 9
- Lim sup of Random Variables and Events
- In a model category, is the full subcategory of fibrant objects a reflective subcategory?
- Calculating $\sum_{k=1}^nk(k!)$ combinatorially
- Serre duality as a right adjoint functor
- How to find positive integer solution of bilinear transformation?
- Good books on conic section.
- Example of a complete, non-archimedean ordered field
- What are some good examples for suggestive notation?