Turing's normal numbers: Towards randomness

In a manuscript entitled "A note on normal numbers" and written presumably in 1938 Alan Turing gave an algorithm that produces real numbers normal to every integer base. This proves, for the first time, the existence of computable normal numbers and it is the best solution to date to Borel...

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Detalles Bibliográficos
Autor principal: Becher, V.
Formato: SER
Materias:
Normal numbers
Real number
Number theory
Random processes
Computability and decidability
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03029743_v7318LNCS_n_p35_Becher
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_03029743_v7318LNCS_n_p35_Becher2023-10-03T15:19:24Z Turing's normal numbers: Towards randomness Becher, V. Normal numbers Real number Number theory Random processes Computability and decidability In a manuscript entitled "A note on normal numbers" and written presumably in 1938 Alan Turing gave an algorithm that produces real numbers normal to every integer base. This proves, for the first time, the existence of computable normal numbers and it is the best solution to date to Borel's problem on giving examples of normal numbers. Furthermore, Turing's work is pioneering in the theory of randomness that emerged 30 years after. These achievements of Turing are largely unknown because his manuscript remained unpublished until its inclusion in his Collected Works in 1992. The present note highlights Turing's ideas for the construction of normal numbers. Turing's theorems are included with a reconstruction of the original proofs. © 2012 Springer-Verlag. Fil:Becher, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. SER info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03029743_v7318LNCS_n_p35_Becher
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Normal numbers
Real number
Number theory
Random processes
Computability and decidability
spellingShingle Normal numbers
Real number
Number theory
Random processes
Computability and decidability
Becher, V.
Turing's normal numbers: Towards randomness
topic_facet Normal numbers
Real number
Number theory
Random processes
Computability and decidability
description In a manuscript entitled "A note on normal numbers" and written presumably in 1938 Alan Turing gave an algorithm that produces real numbers normal to every integer base. This proves, for the first time, the existence of computable normal numbers and it is the best solution to date to Borel's problem on giving examples of normal numbers. Furthermore, Turing's work is pioneering in the theory of randomness that emerged 30 years after. These achievements of Turing are largely unknown because his manuscript remained unpublished until its inclusion in his Collected Works in 1992. The present note highlights Turing's ideas for the construction of normal numbers. Turing's theorems are included with a reconstruction of the original proofs. © 2012 Springer-Verlag.
format SER
author Becher, V.
author_facet Becher, V.
author_sort Becher, V.
title Turing's normal numbers: Towards randomness
title_short Turing's normal numbers: Towards randomness
title_full Turing's normal numbers: Towards randomness
title_fullStr Turing's normal numbers: Towards randomness
title_full_unstemmed Turing's normal numbers: Towards randomness
title_sort turing's normal numbers: towards randomness
url http://hdl.handle.net/20.500.12110/paper_03029743_v7318LNCS_n_p35_Becher
work_keys_str_mv AT becherv turingsnormalnumberstowardsrandomness
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