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Simple Nonstandard Analysis and Applications

In: Nonstandard Analysis for the Working Mathematician

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  • Peter A. Loeb

    (University of Illinois, Department of Mathematics)

Abstract

To accommodate readers with little or no background in mathematical logic, this chapter gives a simple construction of a nonstandard number system associated with a very simple system of logic. The simplicity of the system of logic helps to illuminate the way logic is used to obtain mathematical results. It also simplifies the proof of the “transfer principle”, which is the basic Property of nonstandard number systems. The skills the reader needs for more advanced work are developed through applications of this simple system to calculus and elementary real analysis.To accommodate readers with little or no background in mathematical logic, this chapter gives a simple construction of a nonstandard number system associated with a very simple system of logic. The simplicity of the system of logic helps to illuminate the way logic is used to obtain mathematical results. It also simplifies the proof of the “transfer principle”, which is the basic Property of nonstandard number systems. The skills the reader needs for more advanced work are developed through applications of this simple system to calculus and elementary real analysis.

Suggested Citation

  • Peter A. Loeb, 2015. "Simple Nonstandard Analysis and Applications," Springer Books, in: Peter A. Loeb & Manfred P. H. Wolff (ed.), Nonstandard Analysis for the Working Mathematician, edition 2, chapter 0, pages 3-36, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-7327-0_1
    DOI: 10.1007/978-94-017-7327-0_1
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