MathOverflow

Recall that a finiteness class is a collection of sets satisfying closure under subsets and equipotence, including all the finite sets, and excluding $\omega$. $\mathbf{Fin}$ is the finiteness class consisting of all the finite sets. Under choice, the...

Fix an open set $U\subseteq \mathbb{C}$. Let $C(U)$ denote all continuous $f:U\to\mathbb{C}$ and $H(U)$ denote all holomorphic $f:U\to\mathbb{C}$. Equip $C(U)$ with compact-open topology, and note that $C(U)$ is a Fréchet space, $f_n\to f$ in this topology...

The following sum has an elegant representation in terms of Riemann Zeta functions:$$\mathcal{E}_1(1)=\sum_{n=1}^{\infty} \frac{1}{n^1 \left(n+1\right)}= 1$$$$\mathcal{E}_1(a) = \sum_{n=1}^{\infty} \frac{1}{n^a \left(n+1\right)} = (-1)^{a-1} + \sum_...

Let $f(n)$ be an integer function such that $$ f(n) = \sum\limits_{i=1}^{n} \sum\limits_{j=1}^{i} \sum\limits_{k=1}^{j} [(3ijk - (ij + ik + jk)) = n]. $$
Here square bracket denotes Iverson bracket.
I conjecture that if $f(n) = 0$, then $2n+1$ is always prime....