Non-diophantine Arithmetics In Mathematics, Physics And Psychology
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A01=Marek Czachor
A01=Mark Burgin
Abstract
Action
Addition
Algebra
Archimedean Property
Arithmetic
Author_Marek Czachor
Author_Mark Burgin
Axiom
Cantor Set
Category=PBH
Complex Numbers
Correspondence Principle
Culture
Differentiation
Dimension
Diophantine
Division
Embedding
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equality
Equivalence
Euclidean
Fiber Space
Fourier Transform
Fractal
Geometry
History
Humanities
Identity
Integration
Invariance
Koch Curve
Light Cone
Linear Space
Linear Transformation
Manifold
Mathematics
Matrix
Measurement
Multifractal
Multiplication
Natural Numbers
Newtonian
Non-Diophantine
Non-Euclidean
Non-Newtonian
Number
Number Theory
Numerical
Operation
Philosophy
Physics
Prearithmetic
Probability
Projectivity
Psychology
Psychometric Function
Psychophysics
Quantum Mechanics
Quasilinear Space
Real Numbers
Relativity
Scalar Product
Sensitivity
Sensory Scales
SierpiA...A
Sierpinski Set
Sierpiński Set
Skew
ski Set
Space
Space-Time
Structure
Subarithmetic
Subprearithmetic
Subtraction
Technology
Variable
Vector
Vector Space
Whole Numbers
Product details
- ISBN 9789811214301
- Publication Date: 25 Nov 2020
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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For a long time, all thought there was only one geometry — Euclidean geometry. Nevertheless, in the 19th century, many non-Euclidean geometries were discovered. It took almost two millennia to do this. This was the major mathematical discovery and advancement of the 19th century, which changed understanding of mathematics and the work of mathematicians providing innovative insights and tools for mathematical research and applications of mathematics.A similar event happened in arithmetic in the 20th century. Even longer than with geometry, all thought there was only one conventional arithmetic of natural numbers — the Diophantine arithmetic, in which 2+2=4 and 1+1=2. It is natural to call the conventional arithmetic by the name Diophantine arithmetic due to the important contributions to arithmetic by Diophantus. Nevertheless, in the 20th century, many non-Diophantine arithmetics were discovered, in some of which 2+2=5 or 1+1=3. It took more than two millennia to do this. This discovery has even more implications than the discovery of new geometries because all people use arithmetic.This book provides a detailed exposition of the theory of non-Diophantine arithmetics and its various applications. Reading this book, the reader will see that on the one hand, non-Diophantine arithmetics continue the ancient tradition of operating with numbers while on the other hand, they introduce extremely original and innovative ideas.
