Simple Nonstandard Analysis and Applications

Peter A. Loeb ()
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Peter A. Loeb: University of Illinois, Department of Mathematics

Chapter Chapter 1 in Nonstandard Analysis for the Working Mathematician, 2015, pp 3-36 from Springer

Abstract: 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.

Keywords: Nonstandard Analysis; Transfer Principle; Elementary Real Analysis; Free Ultrafilter; Hyperfinite Set (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-7327-0_1

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DOI: 10.1007/978-94-017-7327-0_1

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