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InfobioticsNumbers and Measures

Infobiotics: Numbers and Measures [Numbers are the essence of any mathematization process. They measure entities, but also provide rigorous frameworks for analyzing the notion of infinity; the set of natural numbers is the first example of infinity. Finiteness and infinity, which very often appear in dialectic aporias, underly the essence of mathematics. Numbers are essential to the notion of population, and are intrinsically related to computation processes. In this chapter, after a brief section on sets and functions, the essentials of numerical systems will be outlined, by emphasizing the concepts that are most relevant for discrete structures. Then, the principle of induction, and basic topics of arithmetic and logic will be presented. Two sections conclude the chapter: one on series and growths (with numbers related to time, space, and matter aggregation), the other one on basic dynamical concepts.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

InfobioticsNumbers and Measures

Part of the Emergence, Complexity and Computation Book Series (volume 3)
Manca, Vincenzo
Infobiotics — Jan 1, 2013
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57 pages

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Publisher
Springer Berlin Heidelberg
Copyright
© Springer-Verlag Berlin Heidelberg 2013
ISBN
978-3-642-36222-4
Pages
215 –271
DOI
10.1007/978-3-642-36223-1_5
Publisher site
See Chapter on Publisher Site

Abstract

[Numbers are the essence of any mathematization process. They measure entities, but also provide rigorous frameworks for analyzing the notion of infinity; the set of natural numbers is the first example of infinity. Finiteness and infinity, which very often appear in dialectic aporias, underly the essence of mathematics. Numbers are essential to the notion of population, and are intrinsically related to computation processes. In this chapter, after a brief section on sets and functions, the essentials of numerical systems will be outlined, by emphasizing the concepts that are most relevant for discrete structures. Then, the principle of induction, and basic topics of arithmetic and logic will be presented. Two sections conclude the chapter: one on series and growths (with numbers related to time, space, and matter aggregation), the other one on basic dynamical concepts.]

Published: Jan 1, 2013

Keywords: Natural Number; Arithmetical Progression; Discrete Dynamical System; Fibonacci Sequence; Positional Representation

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