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The Nature of Numbers: Real Computing.
- Source :
- Journal of Humanistic Mathematics; Jan2022, Vol. 12 Issue 1, p317-347, 31p
- Publication Year :
- 2022
-
Abstract
- While studying the computable real numbers as a professional mathematician, I came to see the computable reals, and not the real numbers as usually presented in undergraduate real analysis classes, as the natural culmination of my evolving understanding of numbers as a schoolchild. This paper attempts to trace and explain that evolution. The first part recounts the nature of numbers as they were presented to us grade-school children. In particular, the introduction of square roots induced a step change in my understanding of numbers. Another incident gave me insight into the brilliance of Alan Turing in his paper introducing both the computable real numbers and his famous 'Turing machine". The final part of this paper describes the computable real numbers in enough detail to supplement the usual undergraduate real analysis class. An appendix presents programs that implement the examples in the text. [ABSTRACT FROM AUTHOR]
- Subjects :
- REAL numbers
TURING machines
SQUARE root
MATHEMATICIANS
SCHOOL children
Subjects
Details
- Language :
- English
- ISSN :
- 21598118
- Volume :
- 12
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of Humanistic Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 155095835
- Full Text :
- https://doi.org/10.5642/jhummath.202201.25