Skip to main content
SpringerLink
Log in

The infidel is innocent

  • Article
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Annotated Bibliography

  • Bishop Berkeley, The analyst: A discourse addressed to an infidel mathematician,The World of Mathematics, vol. 1 (J. R. Newman, ed.), London: Allen and Unwin (1956), 288–293.A thin succulent layer of mathematics with a strong sprinkling of invective, steeped in a vitriolic sauce of sarcasm. Brilliant!!

    Google Scholar 

  • M. Diener, The canard unchainedor how fast/slow dynamical systems bifurcate,Mathematical Intelligencer 6, no. 3 (1984), 38–49.A canny introduction to duck-hunting.

    Article  MATH  MathSciNet  Google Scholar 

  • S. Haack,Philosophy of Logics, Cambridge: Cambridge University Press (1978).Discusses some of the problems with second-order logic and gives the basis for the language used in Section 3.

    Book  Google Scholar 

  • A. E. Hurd (ed.),Nonstandard Analysis-RecentDevelopments, New York: Springer-Verlag (1983).A series of papers (all quite technical) on recent uses of Robinson’s work. Includes a paper by Richter and Szabo on program verification (cf. Section 5).

    MATH  Google Scholar 

  • A. E. Hurd and P. A. Loeb,An Introduction to Nonstandard Real Analysis, London: Academic Press (1985).Chapter 1 contains the construction on which Section 3 was based.

    MATH  Google Scholar 

  • H. J. Keisler,Foundations of Infinitesimal Calculus, Boston: Prindle, Weber and Schmidt (1976).The definitive book on the teaching and understanding of non- standard analysis.

    MATH  Google Scholar 

  • R. Lutz and M. Goze,Nonstandard Analysis: A Practical Guide with Applications, New York: Springer-Verlag (1981).A chirpy, if technical, exploration of non-standard analysis. Good humour let down by poor English!Chapter IV.8 discusses canards (cf. Section 5).

    Book  MATH  Google Scholar 

  • A. Robinson,Non-Standard Analysis, Amsterdam: North-Holland (1966).The original text upon which all of the theory is built.

    MATH  Google Scholar 

  • M. Spivak,Calculus, New York: Benjamin (1967).The introductory text to university-level analysis. The New English bible of the Quasi-religious Sect!

  • I. Stewart,The Problems of Mathematics, Oxford: Oxford University Press (1987).Chapter 7 introduces the subject for the beginner.

    MATH  Google Scholar 

  • K. D. Stroyan and W. A. J. Luxemburg,An Introduction to the Theory of Infinitesimals, New York: Academic Press (1976).Pitched highly, but contains a good ultrafilter construction in chapter 1.

    Google Scholar 

  • D. O. Tall,Infinitesimals Constructed Algebraically and Interpreted Geometrically, Coventry: University of Warwick, preprint (1979).Gives a construction of another extension containing infinitesimals with a neat way of visualising them.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tudor Court, Wattisfield Road, Walsham le Willows, Bury St. Edmunds, IP31 3BD, Suffolk, UK

    Adrian P. Simpson

Authors
  1. Adrian P. Simpson
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Simpson, A.P. The infidel is innocent. The Mathematical Intelligencer 12, 43–51 (1990). https://doi.org/10.1007/BF03024016

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03024016

Keywords

Search

Navigation