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Monotonically Computable Real Numbers (2001)
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| Citations: | 6 - 4 self |
BibTeX
@MISC{Rettinger01monotonicallycomputable,
author = {Robert Rettinger and Xizhong Zheng and Romain Gengler and Burchard von Braunmühl},
title = {Monotonically Computable Real Numbers},
year = {2001}
}
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Abstract
A real number x is called k-monotonically computable (k-mc), for constant k> 0, if there is a computable sequence (xn)n∈N of rational numbers which converges to x such that the convergence is k-monotonic in the sense that k · |x−xn | ≥ |x−xm | for any m> n and x is monotonically computable (mc) if it is k-mc for some k> 0. x is weakly computable if there is a computable sequence (xs)s∈N of rational numbers converging to x such that the sum s∈N |xs − xs+1 | is finite. In this paper we show that all mc real numbers are weakly computable but the converse fails. Furthermore, we show also an infinite hierarchy of mc real numbers.
