The Dynamics in the Soft Numbers Coordinate System

Authors

  • Moshe Klein Tel Aviv University
  • Oded Maimon Tel Aviv University

DOI:

https://doi.org/10.24297/jam.v18i.8531

Keywords:

Soft Logic, Soft Number, Coordinate system, plane strip, soft function, dynamics, recursive process, fractel, Mandelbrot, dynamics set

Abstract

"Soft Logic" extends the number 0 from a single point to a continuous line, which we term "The zero axis". One of the modern science challenges is finding a bridge between the real world outside the observer and the observer's inner world. In “Soft Logic” we suggested a constructive model of bridging the two worlds by defining, on the base of the zero axis, a new kind of numbers, which we called ‘Soft Numbers’.

Inspired by the investigation and visualization of fractals by Mandelbrot, within the investigation of the dynamics of some special function of a complex variable on the complex plane, we investigate in this paper the dynamics of soft functions on the plane strip with a special coordinate system. The recursive process that creates this soft dynamics allows us to discover new dynamics sets in a plane.

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Author Biographies

Moshe Klein, Tel Aviv University

Tel Aviv University

Oded Maimon, Tel Aviv University

Tel Aviv University

References

Dascal, M., (Ed.) "Leibniz: What Kind of Rationalist?" Logic, Epistemology, and the Unity of Science, Vol. 13, Springer Netherlands.(2008)

Datta, P.K., "National mathematics year: A tribute to Srinivasa Ramanujan" Science and Culture, Vol. 79, Nos 3-4, pp. 158-162, (2013)

Klein, M. and Maimon, O. , "The mathematics of Soft Logic", IOP second international conference on mechanical engineering and automation science. Japan (2016)

Klein, M. and Maimon, O., "Soft Logic and Soft Numbers", Pragmatics& cognition, John Benjamins Publishing Company. (2016)

Klein, M. and Maimon, O., "Axioms of Soft Logic", "p-Adic Numbers, Ultrametric Analysis and Applications", Volume 11, No 3,pp.205-215. (2019)

Klein, M. and Maimon, O., " Non-commutative Soft Logic" Submitted for publication. (2019)

Mandelbrot, B., "Fractals and Chaos", Springer (2004)

Robinson, A., "Non-Standard analysis", Princeton Landmarks in mathematics. (1960)

Published

2020-01-04

How to Cite

Klein, M., & Maimon, O. (2020). The Dynamics in the Soft Numbers Coordinate System. JOURNAL OF ADVANCES IN MATHEMATICS, 18, 1-17. https://doi.org/10.24297/jam.v18i.8531

Issue

Section

Articles