On the Significance of Digits in Interval Notation

Details On the Significance of Digits in Interval Notation On the Significance of Digits in Interval Notation

2002-01-17

arxiv.org/abs/cs/0201015v1

Computer Science

Numerical Analysis

11 pages, LaTeX

Scientific paper

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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