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Lines missing every random point1

Article type: Research Article

Authors: Lutz, Jack H. | Lutz, Neil

Affiliations: Department of Computer Science, Iowa State University, Ames, IA 50011, USA . lutz@cs.iastate.edu | Department of Computer Science, Rutgers University, Piscataway, NJ 08854, USA . njlutz@cs.rutgers.edu

Abstract: We prove that there is, in every direction in Euclidean space, a line that misses every computably random point. We also prove that there exist, in every direction in Euclidean space, arbitrarily long line segments missing every double exponential time random point.

Keywords: Randomness, algorithmic geometric measure theory, computable analysis

DOI: 10.3233/COM-150038

Journal: Computability, vol. 4, no. 2, pp. 85-102, 2015

Published: 2015
Price: EUR 27.50
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