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Revision(s):

Revision #1 to TR14-015 | 24th July 2014 02:50

Lines Missing Every Random Point

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Revision #1
Authors: Jack H. Lutz, Neil Lutz
Accepted on: 24th July 2014 02:50
Downloads: 334
Keywords: 


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.



Changes to previous version:

Added a section: "Betting in Doubly Exponential Time."


Paper:

TR14-015 | 24th January 2014 20:36

Lines Missing Every Random Point





TR14-015
Authors: Jack H. Lutz, Neil Lutz
Publication: 31st January 2014 13:00
Downloads: 1075
Keywords: 


Abstract:

This paper proves that there is, in every direction in Euclidean space, a line that misses every computably random point. Our proof of this fact shows that a famous set constructed by Besicovitch in 1964 has computable measure 0.



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