A Technical Note in awe of Nonstandard Analysis

Alagu. S; R. Kala

doi:https://doi.org/10.14445/22315373/IJMTT-V57P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 57 | Number 1 | Year 2018 | Article Id. IJMTT-V57P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V57P507

A Technical Note in awe of Nonstandard Analysis

Alagu. S, R. Kala

Citation :

Alagu. S, R. Kala, "A Technical Note in awe of Nonstandard Analysis," International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 1, pp. 56-58, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P507

Abstract

Nonstandard analysis is a branch of Mathematics introduced by Abraham Robinson in 1966. In 1977, Edward Nelson[4] gave an axiomatic approach to Non-standard analysis. In many instances, analysis on infinite sets can be reduced to a finiteness argument using Nonstandard methods. In this expository article, we present an introduction to the theory and atleast twice make an observation that numbers within our reach are "finitely many".

Keywords

Nonstandard analysis, Continuous function.

References

[1] Abraham Robinson, Nonstandard Analysis, North Holland Publishing Company, 1966.
[2] A.E.Hurd and P.A.Loeb, An Introduction to Non Standard Real Analysis, Academic Press, 1985.
[3] Alain Robert, Nonstandard Analysis, John Wiley and sons, 1985.
[4] Edward Nelson, Internal Set theory, a new approach to NSA, Bull. Amer. Math. Soc., 83 (1977), pp.1165-1198.