MathOverflow

While I fully understand and support the community's strict ban on completely AI-generated content (to prevent low-quality spam and hallucinated proofs), I would like to propose a discussion regarding a more nuanced policy on how users interact with...

Let $\mathcal P$ denote the set of prime numbers, and consider
$N =\frac{1}{1-\displaystyle\sum_{p\in\mathcal P}2^{-p}}$
Numerically, the binary expansion of $N$ appears to behave like that of a base-$2$ normal number. For example, among the first $10^6$ binary digits, the frequencies of $0$ and $1$, and more generally of short binary blocks, are close to the frequencies...

Given $n$ pairwise coprime natural numbers $m_{1}, \dots, m_{n}$ with remainders $y_{i}$, for all $i \leq n$. Furthermore, we have a target interval $I := \left[ a, b \right]$, with $1 \leq a < b \leq M$, $M := \prod_{i = 1}^{n} m_{i}$.
The task is, to find all tuples $T := \left(y_{1}, \dots, y_{n}\right)$ such that...

Examples of infinite dimensional involutions
Edit 2/25/23, as suggested by YCOR below: (Start)
The first return on a Google search on involution--from late Latin 'a rolling up'--gives the Oxford language definition of involution as