The Challenges of Multivalued "Functions"
Reference:
Davenport, J., 2010. The Challenges of Multivalued "Functions". Lecture Notes in Computer Science, 6167, pp. 1-12.
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Official URL:
http://dx.doi.org/10.1007/978-3-642-14128-7_1
Abstract
Although, formally, mathematics is clear that a function is a single-valued object, mathematical practice is looser, particularly with n-th roots and various inverse functions. In this paper, we point out some of the looseness, and ask what the implications are, both for Artifcial Intelligence and Symbolic Computation, of these practices. In doing so, we look at the steps necessary to convert existing texts into (a) rigorous statements (b) rigorously proved statements. In particular we ask whether there might be a constant "de Bruijn factor" [18] as we make these texts more formal, and conclude that the answer depends greatly on the interpretation being placed on the symbols.
Details
| Item Type | Articles |
| Creators | Davenport, J. |
| DOI | 10.1007/978-3-642-14128-7_1 |
| Departments | Faculty of Science > Computer Science |
| Publisher Statement | AISC2010-submitted.pdf: The original publication is available at www.springerlink.com; Springer-AISC.pdf: The original publication is available at www.springerlink.com |
| Refereed | No |
| Status | Published |
| ID Code | 18792 |
| Additional Information | Invited talk at Artificial Intelligence and Symbolic Computation 2010, part of the Conferences in Intelligent Mathematics 2010, 4-10 July 2010. Paris, France. |
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