Intereting Posts

How do I know which of these are mathematical statements?
Evaluate $\sum\limits_{k=0}^n \binom{n}{k}$ combinatorially
Show $\lim\limits_{n\rightarrow\infty}n\left(\frac{1}{n}\sum_{i=1}^{n}f\left(\frac{i}{n}\right)-\int_{0}^{1}f(x)dx\right)=\frac{f(1)-f(0)}{2}$
Why does this $u$-substitution zero out my integral?
Interesting calculus problems of medium difficulty?
Convergence of a compound sequence
Lambert's Original Proof that $\pi$ is irrational.
If $a_n=n^2+20$ and $d_n$ denotes the greatest common divisor of $a_n$ and $a_{n+1}$ then show that $d_n$ divides 81
$\lim_{x \to 0} \dfrac{f(x)-g(x)}{g^{-1}(x)-f^{-1}(x)} = 1$ for any $f,g \in C^1$ that are tangent to $\text{id}$ at $0$ with some simple condition
Proof by induction regarding injections and part of the pigeonhole principle
Eigenvalues appear when the dimension of the Prime Index Matrix is a prime-th prime. Why?
A comparison between the fundamental groupoid and the fundamental group
How find this equation $\prod\left(x+\frac{1}{2x}-1\right)=\prod\left(1-\frac{zx}{y}\right)$
How to prove that a simple graph having 11 or more vertices or its complement is not planar?
Artinian affine $K$-algebra

Let $G$ be a finite semi-group with identity such that it has only one idempotent.Is $G$ a group?

It only remains to show that for any $a\in G$ $\exists b\in G$ such that $ab=ba=e$ where $e$ is the identity of $G$

Also $e$ is the only idempotent of $G$ .How to proceed next?

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- Subgroup of $\mathbb{Q}$ with finite index

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- What is the intersection of all Sylow $p$-subgroup's normalizer?
- A general element of U(2)
- Divisible abelian $q$-group of finite rank

Show that for every $x\in G$, there is an $n\in \Bbb N$ such that $x^n$ is idempotent. Then you can claim that for every $x\in G$, some power of $x$ equals $e$.

- Vandermonde identity corollary $\sum_{v=0}^{n}\frac{(2n)!}{(v!)^2(n-v)!^2}={2n \choose n}^2$
- Advanced algebraic topology topics overview
- An integral of a rational function of logarithm and nonlinear arguments
- Reflexive but not separable space
- Conics definition from Lens formula
- What does actually probability mean?
- The annihilator of an intersection is the sum of annihilators
- One Question about the Fubini's Theorem
- Is it valid to write $1 = \lim_{x \rightarrow 0} \frac{e^x-1}{x} = \frac{\lim_{x \rightarrow 0} (e^x) -1}{\lim_{x \rightarrow 0} x}$?
- Theorem 8.17 , Chapter II, Hartshorne
- Simple series convergence/divergence: $\sum_{k=1}^{\infty}\frac{2^{k}k!}{k^{k}}$
- A UFD for which the related formal power series ring is not a UFD
- What are the conditions for integers $D_1$ and $D_2$ so that $\mathbb{Q} \simeq \mathbb{Q}$ as fields.
- If the positive series $\sum a_n$ diverges and $s_n=\sum\limits_{k\leqslant n}a_k$ then $\sum \frac{a_n}{s_n}$ diverges as well
- Short proof for the non-Hamiltonicity of the Petersen Graph