data obtained in association with many real-life random experiments from different fields cannot be perfectly/exactly quantified.hspace{.1cm}often the underlying imprecision can be suitably described in terms of fuzzy numbers/values. for these random experiments, the scale of fuzzy numbers/values enables to capture more variability and subjectivity than that of categorical data, and more accura...

Instances of such “arithmetic 1-extensions” naturally arise in arithmetic geometry and in geometry of numbers. In this talk we discuss an arithmetic analog of the Enriques-Severi-Zariski Lemma in classical algebraic geometry: namely, if X is a projective integral scheme over SpecZ and if the class of EQ in the classical extension group Ext1XQ(EQ, FQ) does not vanish, then for “many” points P in...

In this paper, we study arithmetic properties of weighted Catalan numbers. Previously, Postnikov and Sagan found conditions under which the 2-adic valuations numbers are equal to We obtain same result weaker by considering a map from class functions integers. These methods also extended q-weighted numbers, strengthening previous Konvalinka. Finally, prove some results on periodicity modulo an i...

The purpose of this paper is to introduce the idea how construct transfinite numbers and study arithmetic. research method used a literature review, which involves collecting various sources such as scientific papers books related Cantorian set theory, infinity, ordinal or arithmetic, well connection between infinity theology. also constructing objects study, namely finite ordinals ordinals, ex...

Inspired by a mathematical riddle involving fuses, we define the "fusible numbers" as follows: $0$ is fusible, and whenever $x,y$ are fusible with $|y-x|<1$, number $(x+y+1)/2$ also fusible. We prove that set of numbers, ordered usual order on $\mathbb R$, well-ordered, type $\varepsilon_0$. Furthermore, density numbers along real line grows at an incredibly fast rate: Letting $g(n)$ be largest...