Erdős proved that any real number can be written as a sum, and a product, of two Liouville numbers. Motivated by these results, we study sumsets of classes of real numbers with prescribed (or bounded) irrationality exponents. We show that such sumse...
The purpose of this note is to introduce a trick which relates the (non)-vanishing of the top-dimensional $\ell^2$-Betti numbers of actions with that of sub-actions. We provide three different types of applications: we prove that the $\ell^2$-Betti n...
The purpose of this note is to point out that the theory of expander graphs leads to an interesting test whether $n$ real numbers $x_1, \dots, x_n$ could be $n$ independent samples of a random variable. To any distinct, real numbers $x_1, \dots, x_n$...
Unums (universal numbers) are a family of number formats and arithmetic for implementing real numbers on a computer, proposed by John L. Gustafson in
Jul 20, 2021 · I searched the meaning of "thousands" and "hundreds" hundredsThe numbers from 100 to 999. (Lexico Dictionary) thousands The numbers from one thousand to 9,999. so I got to wonder in …
recursive numbers, effective numbers, computable reals, or recursive reals. The concept of a computable real number was introduced by Émile Borel in 1912
A real number is a rule that, when provided with a rational interval, answers Yes or No depending on if the real number ought to be considered to be in the given interval. Since the goal is to define the real numbers, this can only motivate the defin...
We investigate the $a$-numbers of $\mathbb{Z}/p^2\mathbb{Z}$-covers in characteristic $p>2$ and extend a technique originally introduced by Farnell and Pries for $\mathbb{Z}/p\mathbb{Z}$-covers. As an application of our approach, we demonstrate that...
We prove that the Lehmer mean function of two or three positive numbers has always one and only one inflection point. We further show that in case of two numbers, the inflection point is $p^\star = 1$, and we discuss the location of the inflection po...
Aug 1, 2025 · Free online math calculator to add, subtract, multiply and divide positive and negative numbers. Online decimal calculator to find sum, difference and products of numbers.
What is a counting number in Maths? In Mathematics, counting numbers are natural numbers, that are used to count anything.
In this brief note, we clarify certain aspects related to the magnetic (i.e., odd parity or axial) tidal Love numbers of a star in general relativity. Magnetic tidal deformations of a compact star had been computed in 2009 independently by Damour and...
Aug 19, 2010 · Magic numbers are special value of certain variables which causes the program to behave in an special manner. For example, a communication library might take a Timeout parameter …
Feb 13, 2026 · Division in maths is a way of sharing or grouping numbers into equal parts. In other words, division is used for finding the smaller group into which a large group of numbers can be …
We generalize Luck's Theorem to show that the L^2-Betti numbers of a residually amenable covering space are the limit of the L^2-Betti numbers of a sequence of amenable covering spaces. We show that any residually amenable covering space of a finit...
Suppose X is any finite complex with vanishing L^2 Betti number. We prove upper bounds on the Betti numbers for regular coverings of X, sublinear in the order of covering. The bounds are sensitive to the Novikov-Shubin invariants of X, and are impr...
We show that the Betti numbers of a local system on the complement of an essential complex hyperplane arrangement are maximized precisely when the local system is constant. This result answers positively a recent question of Yoshinaga and the first a...
An asymptotic formula is given for the number of y-smooth numbers up to x in a Beatty sequence corresponding to an irrational number of finite type....
The maximum possible number of non-overlapping unit spheres that can touch a unit sphere in $n$ dimensions is called kissing number. The problem for finding kissing numbers is closely connected to the more general problems of finding bounds for spher...
In this paper we investigate congruence relationships of particular finite generalized harmonic numbers sums. We suggest more transparent and simpler method to analyse these sums and present several additional results for certain special cases....