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The Hyperreal Line

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Real Numbers, Generalizations of the Reals, and Theories of Continua

Part of the book series: Synthese Library ((SYLI,volume 242))

Abstract

The aim of this article is to explain that the hyperreal line is, what it looks like, and what it is good for. Near the beginning of the article we shall draw pictures of the hyperreal line and sketch its construction as an ultrapower of the real line. In the middle part of the article, we shall survey mathematical results about the structure of the hyperreal line. Near the end, we shall discuss philosophical issues concerning the nature and significance of the hyperreal line.

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Author information

Authors and Affiliations

  1. University of Wisconsin, Madison, USA

    H. Jerome Keisler

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  1. H. Jerome Keisler
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Editor information

Editors and Affiliations

  1. Ohio University, USA

    Philip Ehrlich

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© 1994 Springer Science+Business Media Dordrecht

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Keisler, H.J. (1994). The Hyperreal Line. In: Ehrlich, P. (eds) Real Numbers, Generalizations of the Reals, and Theories of Continua. Synthese Library, vol 242. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8248-3_8

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  • DOI: https://doi.org/10.1007/978-94-015-8248-3_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4362-7

  • Online ISBN: 978-94-015-8248-3

  • eBook Packages: Springer Book Archive

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