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On the Significance of Digits in Interval Notation

2002/01/17 by M. H. van Emden, van Emden, M. H.
Computer Science · Engineering · #B.4.m #Control Systems and Identification #Digital Filter Design and Implementation #FOS: Mathematics #G.1.0 #G.4 #Numerical Analysis (math.NA) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.cs/0201015

openalex publication_date 2002/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To analyse the significance of the digits used for interval bounds, we clarify the philosophical presuppositions of various interval notations. We use information theory to determine the information content of the last digit of the numeral used to denote the interval's bounds. This leads to the notion of efficiency of a decimal digit: the actual value as percentage of the maximal value of its information content. By taking this efficiency into account, many presentations of intervals can be made more readable at the expense of negligible loss of information.

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