Calude,CSStaiger, L2014-01-052014-01-052013CDMTCS Research Reports CDMTCS-448 (2013)1178-3540https://hdl.handle.net/2292/21347We present a systematic comparison between Liouville, computable, Borel normal and Martin-Lof random numbers. The nine non-empty combinations, all small in measure or category, are illustrated with concrete examples. The sets of Liouville numbers and Martin-Lof random numbers are disjoint, thus showing that the irrationality exponent is not a measure of randomness. Finally, we construct the first computable set of correlations appearing in every Martin-Lof random number, but not in all numbers.Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher.https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htmTechnical ReportFields of Research::280000 Information, Computing and Communication SciencesThe author(s)http://purl.org/eprint/accessRights/OpenAccess