Abstract
The classical view of mathematics is essentially descriptive: we try to describe the facts about a static mathematical universe. Thus, for example, we report that every polynomial of odd degree has a root, and that there is a digit that occurs infinitely often in the decimal expansion of π. In opposition to this is the constructive view of mathematics, which focuses attention on the dynamic interaction of the individual with the mathematical universe; in the words of Hao Wang, it is a mathematics of doing, rather than a mathematics of being. The constructive mathematician must show how to construct a root of a polynomial of odd degree, and how to find a digit that occurs infinitely often in the decimal expansion of π.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer Science+Business Media New York
About this chapter
Cite this chapter
Mines, R., Richman, F., Ruitenburg, W. (1988). Sets. In: A Course in Constructive Algebra. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8640-5_1
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8640-5_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96640-3
Online ISBN: 978-1-4419-8640-5
eBook Packages: Springer Book Archive