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Nonstandard Analysis for Some Convergence Sequences Theories Via a Transfer Principle

Jwahir-H-Gdal1
  • 1 University of Bisha, Saudi Arabia
American Journal of Applied Sciences
Volume 18 No. 1, 2021, 33-50

DOI: https://doi.org/10.3844/ajassp.2021.33.50

Submitted On: 3 November 2020 Published On: 9 February 2021

How to Cite: Jwahir-H-Gdal, . (2021). Nonstandard Analysis for Some Convergence Sequences Theories Via a Transfer Principle. American Journal of Applied Sciences, 18(1), 33-50. https://doi.org/10.3844/ajassp.2021.33.50

Abstract

The purpose of this article to introduce nonstandard models for a familiar types of convergent sequences theories through a transfer principle. The nonstandard analysis principle discuss, that any statements on areal system can be extended to a similar structure over larger hyperreal system therefore the results that hold true on the original system, remains true in a hyperreal system if and only if its ∗-transform is true. We apply such technique to transfer a classical proof for real sequences theorems, therefore we obtain an equivalents nonstandard proof   on hyperreal system which is often clear, shorter and uncoblicated.

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Keywords

  • Nonstandard Analysis
  • Hyperreal Numbers
  • ∗-Transform A Transfer Principle
  • Convergence Sequences