Only Intervals Preserve the Invertibility of Arithmetic Operations

Only Intervals Preserve the Invertibility of Arithmetic Operations In standard arithmetic, if we, e.g., accidentally added a wrong number y to the preliminary result x, we can undo this operation by subtracting y from the result x+y. A similar possibility to invert (undo) addition holds for intervals. In this paper, we show that if we add a single non-interval set, we lose invertibility. Thus, invertibility requirement leads to a new characterization of the class of all intervals. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Only Intervals Preserve the Invertibility of Arithmetic Operations

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Publisher
Springer Journals
Copyright
Copyright © 1999 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009982014556
Publisher site
See Article on Publisher Site

Abstract

In standard arithmetic, if we, e.g., accidentally added a wrong number y to the preliminary result x, we can undo this operation by subtracting y from the result x+y. A similar possibility to invert (undo) addition holds for intervals. In this paper, we show that if we add a single non-interval set, we lose invertibility. Thus, invertibility requirement leads to a new characterization of the class of all intervals.

Journal

Reliable ComputingSpringer Journals

Published: Oct 15, 2004

References

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