Nonstandard Analysis for Some Convergence Sequences Theories Via a Transfer Principle
- 1 University of Bisha, Saudi Arabia
Copyright: © 2021 Jwahir-H-Gdal. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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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- Nonstandard Analysis
- Hyperreal Numbers
- ∗-Transform A Transfer Principle
- Convergence Sequences