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Arithmetic is not arithmetic: Paradigm matters for arithmetic effects
CognitionResearch 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 +3 more
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Mathematical Logic Quarterly, 1998
AbstractWe develop arithmetical measure theory along the lines of Lutz [10]. This yields the same notion of measure 0 set as considered before by Martin‐Löf, Schnorr, and others. We prove that the class of sets constructible by r.e.‐constructors, a direct analogue of the classes Lutz devised his resource bounded measures for in [10], is not equal to RE,
Terwijn, S., Torenvliet, L.
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AbstractWe develop arithmetical measure theory along the lines of Lutz [10]. This yields the same notion of measure 0 set as considered before by Martin‐Löf, Schnorr, and others. We prove that the class of sets constructible by r.e.‐constructors, a direct analogue of the classes Lutz devised his resource bounded measures for in [10], is not equal to RE,
Terwijn, S., Torenvliet, L.
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Arithmetic in Peano Arithmetic
2020In 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
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The arithmetic of cuts in models of arithmetic
Mathematical Logic Quarterly, 2013We present a number of results on the structure of initial segments of models of Peano arithmetic with the arithmetic operations of addition, subtraction, multiplication, division, exponentiation and logarithm. Each of the binary operations introduced is defined in two dual ways, often with quite different results, and we attempt to systematise the ...
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SOLVABLE ARITHMETIC GROUPS AND ARITHMETICITY PROBLEMS
International Journal of Mathematics, 1999We 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
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Arithmetic norms and bounds of the arithmetic AN codes
IEEE Transactions on Information Theory, 1970Properties of integers, related to the generation of the arithmetic AN codes, are investigated in this paper. A programmable algorithm for the computation of the binary norm of an arbitrary integer is developed. A table of norms of the natural numbers is generated and from this the distribution of integers of a given norm is found.
Albert C. L. Chiang, Irving S. Reed
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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
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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
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IEEE Transactions on Computers, 1987
We present the design of a VLSI processor which can be programmed to compute the discrete Fourier transform of a sequence of n points and which achieves the theoretical AT2 lower bound of ?(n2) for n ? n where n is an infinite set. Furthermore, since the set n is also sufficiently dense, the processor achieves for any n the theoretical AT2 lower bound ...
Robert Michael Owens, Mary Jane Irwin
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We present the design of a VLSI processor which can be programmed to compute the discrete Fourier transform of a sequence of n points and which achieves the theoretical AT2 lower bound of ?(n2) for n ? n where n is an infinite set. Furthermore, since the set n is also sufficiently dense, the processor achieves for any n the theoretical AT2 lower bound ...
Robert Michael Owens, Mary Jane Irwin
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Journal of Mathematical Sciences, 2021
This long paper is a survey, with some new results, on arithmetical rings, modules, and Bezout rings (not necessarily commutative). The plan of this article is very clear. There is a table of contents which is very useful for the reader. This paper contains 5 chapters.
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This long paper is a survey, with some new results, on arithmetical rings, modules, and Bezout rings (not necessarily commutative). The plan of this article is very clear. There is a table of contents which is very useful for the reader. This paper contains 5 chapters.
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Additive Arithmetic Functions on Arithmetic Progressions
Proceedings of the London Mathematical Society, 1987For 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 ...
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