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Nonstandard Analysis for Some Convergence Sequences Theories Via a Transfer Principle

Jwahir-H-Gdal1
  • 1 University of Bisha, Saudi Arabia

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.

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

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Keywords

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