Abstract
The purpose of this paper is to investigate some problems of using finite (or *finite) computational arguments and of the nonstandard notion of an infinitesimal. We will begin by looking at the canonical example illustrating the distinction between classical and constructive analysis, the Intermediate Value Theorem.
Similar content being viewed by others
References
S. Albeverio, J. E. Fenstad, R. Høegh-Krohn, and T. Lindstrøm, Nomtandard Methods in Stochastic Analysis and Mathematical Physics, Academic Press, Orlando, 1986.
E. Bishop, Foundations of Constructive Analysis, McGraw-Hill, New York, 1967.
E. Bishop and D. Bridges, Constructive Analysis, Springer-Verlag, Berlin, 1985.
A. E. Hurd and P. A. Loeb, An Introduction to Nonstandard Real Analysis, Academic Press, Orlando, 1985.
A. Robinson, Non-Standa Analysis, North-Holland, Amsterdam, 1974.
K. D. Stroyan and W. A. J. Luxemburg, Introduction to the Theory of Infinitesimals, Academic Press, New York, 1976.
F. Wattenberg, Nonstandard topology and extensions of monad systems to infinite points, Journal of Symbolic Logic 36 (1971), pp. 463–476.
F. Wattenberg, Monads of infinite points and finite product spaces, Trans. Amer. Math. Soc. 176 (1973), pp. 351–368.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wattenberg, F. Nonstandard analysis and constructivism?. Stud Logica 47, 303–309 (1988). https://doi.org/10.1007/BF00370558
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00370558