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".

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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.