Universal codes of the natural numbers by Yuval Filmus

“…A code of the natural numbers is a uniquely-decodable binary code of the natural numbers with non-decreasing codeword lengths, which satisfies Kraft's inequality tightly. …”
Get full text

Sums of powers of natural numbers : the pattern of the coefficients / by 195607 Chang, Tian Hock

Mathematical logic with special reference to the natural numbers / by 323173 Steen, Stourton William Peile

Natural Alternatives to Natural Number: The Case of Ratio by Percival G. Matthews, Amy B. Ellis

“…The overwhelming majority of efforts to cultivate early mathematical thinking rely primarily on counting and associated natural number concepts. Unfortunately, natural numbers and discretized thinking do not align well with a large swath of the mathematical concepts we wish for children to learn. …”
Get full text

COUNTABLE COMPACTNESS MODULO AN IDEAL OF NATURAL NUMBERS by Prasenjit Bal, Debjani Rakshit, Susmita Sarkar

Get full text

Continued Fractions of Square Roots of Natural Numbers by L'ubomíra Balková, Aranka Hrušková

“…The second author describes periods and sometimes the precise form of continued fractions of ?N, where N is a natural number. In cases where we have been able to find such results in the literature, we recall the original authors, however many results seem to be new.…”
Get full text

Generating Bijections between HOAS and the Natural Numbers by John Tang Boyland

“…A provably correct bijection between higher-order abstract syntax (HOAS) and the natural numbers enables one to define a ``not equals'' relationship between terms and also to have an adequate encoding of sets of terms, and maps from one term family to another. …”
Get full text

Defining Properties of Primitive Systems of Natural Numbers by S. N. Kyazhin, V. M. Fomichev

Subjects: “…primitive system of natural numbers…”
Get full text

An extended mind perspective on natural number representation by De Cruz, H

“…To explain this difference, I take an extended mind perspective, arguing that the distinctly human ability to use external representations as a complement for internal cognitive operations enables us to represent natural numbers. Reviewing neuroscientific, developmental, and anthropological evidence, I argue that the use of external media that represent natural numbers (like number words, body parts, tokens or numerals) influences the functional architecture of the brain, which suggests a two-way traffic between the brain and cultural public representations.…”

Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture by Ramon Carbó Dorca, Carlos Perelman

“…Using simple arguments derived from the Boolean hypercube configuration, the structure of natural spaces, and the recursive exponential generation of the set of natural numbers, a linear classification of the natural numbers is presented. …”
Get full text

LikeN's - a point of view on natural numbers by Edward Tutaj

“…We define and study some simple structures which we call likens and which are conceptually near to both sets of natural numbers, i.e. N with addition and N*=N\{0} with multiplication. …”
Get full text

Beyond natural numbers: Representation of negative numbers in the parietal cortex by Kristen Pilner Blair, Miriam eRosenberg-Lee, Jessica M Tsang, Daniel L Schwartz, Vinod eMenon

“…Unlike natural numbers, negative numbers do not have natural physical referents. …”
Get full text

On a certain characterisation of the semigroup of positive natural numbers with multiplication by Edward Tutaj

“…The most important examples of likens are clearly the set of natural numbers N with addition and the set of positive natural numbers N* with multiplication, represented by the sequence (ln(n+1))∞ n=0. …”
Get full text

Strategies for Solving Multiplicative Structure Problems with Natural Numbers and Fractions by Cristina Zorrilla, Pedro Ivars, Ceneida Fernández

“…Algorithms were the most commonly used strategy, but other strategies also emerged, depending on the type of number involved (natural numbers or fractions). …”
Get full text

Decidability of the Interval Temporal Logic ABB Over the Natural Numbers by Montanari, A, Puppis, G, Sala, P

From magnitude to natural numbers: A developmental neurocognitive perspective by Kadosh, R, Walsh, V

“…We provide evidence demonstrating that the acquisition of natural numbers depends on magnitude representation and that natural numbers develop from a general magnitude mechanism in the parietal lobes. © 2008 Cambridge University Press.…”

Arithmetic and Boolean Operations on Recursively Run-Length Compressed Natural Numbers by P. Tarau

“…We study arithmetic properties of a new tree-based canonical num- ber representation, recursively run-length compressed natural numbers, defined by applying recursively a run-length encoding of their binary digits. …”
Get full text

About the Entropy of a Natural Number and a Type of the Entropy of an Ideal by Nicuşor Minculete, Diana Savin

“…In this article, we find some properties of certain types of entropies of a natural number. We are studying a way of measuring the “disorder” of the divisors of a natural number. …”
Get full text

Assistance System for the Teaching of Natural Numbers to Preschool Children with the Use of Artificial Intelligence Algorithms by William Villegas-Ch., Angel Jaramillo-Alcázar, Aracely Mera-Navarrete

“…This research was aimed at designing an image recognition system that can help increase children’s interest in learning natural numbers between 0 and 9. The research method used was qualitative descriptive, observing early childhood learning in a face-to-face education model, especially in the learning of numbers, with additional data from literature studies. …”
Get full text

The Interplay Between the Natural Number Bias and Fraction Magnitude Processing in Low-Achieving Students by Frank Reinhold, Andreas Obersteiner, Stefan Hoch, Sarah Isabelle Hofer, Kristina Reiss, Kristina Reiss

Subjects: “…natural number bias…”
Get full text