Results 261 to 270 of about 1,046,535 (320)

Arithmetic in Peano Arithmetic

2020
In this chapter, we take a closer look at Peano Arithmetic (PA) which we have defined in Chapter 1. In particular, we prove within PA some basic arithmetical results, starting with the commutativity and associativity of addition and multiplication, culminating in some results about coprimality.
Lorenz Halbeisen, Regula Krapf
openaire   +1 more source

Arithmetic Permutations

Journal of the London Mathematical Society, 1991
The group \(\hbox{Sym }\mathbb{R}\) of permutations of the set \(\mathbb{R}\) of real numbers is considered in the paper. Let \(P_ 0\) be its subgroup of power functions \(x\mapsto x^{m/n}\) where \(m\), \(n\) are positive odd integers, \(T\) be the subgroup of translations \(x\mapsto x+a\) where \(a\) is a real algebraic number, and \(M\) be the ...
Adeleke, S. A., Glass, A. M. W., Morley, L.   +2 more
openaire   +2 more sources

Arithmetic is not arithmetic: Paradigm matters for arithmetic effects

Cognition
Research on arithmetic uses different experimental paradigms. So far, it is unclear whether these different paradigms lead to the same effects or comparable effect sizes. Therefore, this study explores how different experimental paradigms influence mental arithmetic performance, focusing on understanding the potential differences and similarities in ...
Xinru, Yao, Christina, Artemenko, Yunfeng, He, Hans-Christoph, Nuerk   +3 more
openaire   +2 more sources

Arithmetic Without Algorithms: Language Models Solve Math With a Bag of Heuristics

International Conference on Learning Representations
Do large language models (LLMs) solve reasoning tasks by learning robust generalizable algorithms, or do they memorize training data? To investigate this question, we use arithmetic reasoning as a representative task. Using causal analysis, we identify a
Yaniv Nikankin, Anja Reusch, Aaron Mueller, Yonatan Belinkov   +3 more
semanticscholar   +1 more source

SOLVABLE ARITHMETIC GROUPS AND ARITHMETICITY PROBLEMS

International Journal of Mathematics, 1999
We describe solvable arithmetic groups for which natural rigidity properties hold and solve the arithmeticity problem for the automorphism groups of these arithmetic groups and further prove arithmeticity results for their finite extensions. We also solve the arithmeticity problem for polycyclic groups. We prove that there are non-arithmetic polycyclic
Grunewald, Fritz, Platonov, Vladimir
openaire   +2 more sources

Neural Underpinnings of Numerical and Spatial Cognition: An fMRI Meta-Analysis of Brain Regions Associated with Symbolic Number, Arithmetic, and Mental Rotation.

Neuroscience and Biobehavioral Reviews, 2019
Where and under what conditions do spatial and numerical skills converge and diverge in the brain? To address this question, we conducted a meta-analysis of brain regions associated with basic symbolic number processing, arithmetic, and mental rotation ...
Zachary C K Hawes, H. Sokolowski, Chuka Ononye, D. Ansari   +3 more
semanticscholar   +1 more source

Finite Precision Rational Arithmetic: An Arithmetic Unit

IEEE Transactions on Computers, 1983
The foundations of an arithmetic unit performing the add, subtract, multiply, and divide operations on rational operands are developed. The unit uses the classical Euclidean algorithm as one unified algorithm for all the arithmetic operations, including rounding.
Kornerup, Peter, Matula, David W.
openaire   +1 more source

Additive Arithmetic Functions on Arithmetic Progressions

Proceedings of the London Mathematical Society, 1987
For an additive arithmetic function f, and positive integer D, let E(x,D) be \[ \max_{y\leq x}\max_{(r,D)=1}| \sum_{n\leq y,\quad n\equiv r (mod D)}f(n)-(1/\phi (D))\sum_{n\leq y,\quad (n,D)=1}f(n)|. \] Strengthening results from Chapter 7 of his monograph ''Arithmetic functions and integer products'' (1985; Zbl 0559.10032), the author proves that for ...
openaire   +2 more sources

Children and Arithmetic

Journal of Child Psychology and Psychiatry, 1995
Abstract The development of children's understanding of mathematical relations and of their grasp of the number system is described. It is discussed that children easily recognise one‐way pan‐pan relations but that the number system at first causes them difficulty. Children's relational understanding allows them
openaire   +2 more sources

Arithmetic Theory of Arithmetic Surfaces

The Annals of Mathematics, 1989
is a proper smooth surface over a finite field F,. The primary purpose of this paper is to develop arithmetic theory of the Brauer group Br(K) of K. Here we have to assume that the ring J(X, (x) of the regular functions on X has no embedding into R. In general all results hold true modulo 2-torsion.
openaire   +1 more source