22 problems

Consistency conjecture. It is consistent with ZFC that there are no compact hyperfinite Loeb spaces in any nonstandard universes.

Let $r,s\in\mathbb R\setminus\mathbb Q$ be irrational numbers, and let ${}^{\ast}\mathbb Z_r$ and ${}^{\ast}\mathbb Z_s$ denote their associated groups of nonstandard diophantine a…

Let $\boe\res\boldsymbol{N}$ denote the relation on $\boldsymbol{N}$ defined by $x\boe y$ if there is a Borel bijection from $[0,x)$ onto $[0,y)$. Let…

Let $u$ be a solution of the grid-function formulation, let $u^{!astphi(u)}{(t,x)}$ denote the associated measure, let $Omega{mathbb{X}}$ be the hyperfinite spatial domain, and le…

Let $\mathbb{R^{Z_<}}$ be the set equipped with the $\mathfrak{e}$-topology, and call a sequence in $\mathbb{R^{Z_<}}$ hyper-Cauchy when for every $\mathfrak{e}\in\mathbb{R^{Z_<}}$…

Let $h$ be the grid function considered in Lemma, and let $\mathbb{D}$ denote the grid derivative appearing there. The source establishes the identities … and the corresponding sta…

Let $\Omega$ be a measurable set of finite Lebesgue measure, let $l$ be an embedding of distributions into grid functions, and let $l'$ be the embedding of grid functions into…

Classical Nonstandard Analysis uses the predicate “$x$ is standard” to distinguish standard from nonstandard objects. A proof can be viewed as consisting of an initial part using T…

The paper considers a functional $\Theta$ and, for each function $f$ of type $1$, an arithmetical map $f\mapsto F_f$ such that $\Theta(F_f)$ is the characteristic function of a set…

Generality conjecture. The “one-size-fits-all” provided by the template ${\mathfrak{CI}}$ is very general and will produce terms of acceptable complexity.

Let $\mathbb{N}_{\infty}$ denote the infinite integers. Infinite-integer ratio transfer conjecture. There exist ratios of infinite integers of the form … that can be transferred to…

Infinite-interval comparison conjecture. One has

L-function comparison conjecture. Every L-function at infinity is ultimately continuous and monotonic. If $f$ and $g$ are L-functions, then in

Let $f(x)$ be a function such that … and let $k=d4a$ denote an infinite iteration index. Iterated-logarithm infinity conjecture. When $x$ reaches infinity before $k$, one has … The…

Let $*G$ denote the gossamer numbers and let $d53f$ denote the real numbers. Cardinality conjecture. The cardinality of the gossamer numbers is larger than the cardinality of the r…

Let a continuous curve be given, and consider a uniform Riemann sum for it together with a Riemann sum whose limit is infinite. Asymptotic equivalence conjecture. A uniform Riemann…

BISH classification conjecture. There are two categories:

Uniformity conjecture. One can choose $m$ and $n$ depending additionally on $\delta$.

Let $\theta$ and $\eta$ be real numbers, let $\Bumpeq$ denote their equivalence relation, and let ${}^{\ast}\mathbb Z(\theta)$ and ${}^{\ast}\mathbb Z(\eta)$ be their Diophantine a…

Let $\text{\usefont{U}{euf}{m}{n}W}_{\infty}$ denote the class of real numbers with the strong ideological generation property. Strong ideological generation conjecture.…

Let $a_1,a_2,a_3,\ldots$ be a sequence of complex numbers, and let $\{b_n\}$ be its partial sum sequence, assumed to be bounded. Choose a hyperreal number system and define…

Let ${}^{\bullet}\wp^{\mathrm{nc}}_{\mu,\theta}$ and ${}^{\bullet}\wp'_{\mu,\theta}$ be the quantum nonstandard Weierstrass function and its derivative, and let…