5 problems

Let $Q$ be a basic sequence. Hausdorff-dimension separation conjecture. If $Q$ is infinite in limit and $t$-divergent, and $\{1,\ldots,t\}=A\mathbin{\dot\cup}B$, then the set … has…

Suppose that $\mathbb{N}=A\mathbin{\dot\cup}B$ is a partition of the natural numbers. Let $Q$ be a basic sequence, and say that it is fully divergent when the relevant divergence c…

Let $t\geq2$ be an integer and suppose that $\{1,\ldots,t\}=A\mathbin{\dot\cup}B$. Let $Q$ be a basic sequence, and say that it is $t$-divergent when the relevant divergence condit…

Small-perturbation solvability conjecture. Whenever $\lVert\vec{\epsilon}\rVert$ is sufficiently small, this system has a solution

Let $Q=(q_n)_{n\geq 1}$ be a basic sequence that is infinite in limit and fully divergent of type I. A real number is $Q$-normal if it belongs to $\mathscr{N}(Q)$, and is AP $Q$-ab…