Computable number (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Computable number" in English language version.

Last modified: 09:02:39, 27 August 2026 (UTC)

Ref.Un. Ref.Website

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1111doi.org

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44semanticscholar.org

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33ams.org

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33jstor.org

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33web.archive.org

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22eudml.org

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11abelard.org

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11archive.org

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11worldcat.org

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11books.google.com

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11rero.ch

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11arxiv.org

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11github.com

380^th place

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11springer.com

182^nd place

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abelard.org (Global: low place; English: low place)

Turing (1936). Turing, A. M. (1936). "On Computable Numbers, with an Application to the Entscheidungsproblem". Proceedings of the London Mathematical Society. Series 2. 42 (1) (published 1937): 230–65. doi:10.1112/plms/s2-42.1.230. S2CID 73712.
Turing, A. M. (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction". Proceedings of the London Mathematical Society. Series 2. 43 (6) (published 1937): 544–6. doi:10.1112/plms/s2-43.6.544. Computable numbers (and Turing's a-machines) were introduced in this paper; the definition of computable numbers uses infinite decimal sequences.

ams.org (Global: 434^th place; English: 249^th place)

mathscinet.ams.org

Pour-El, Marian Boykan; Richards, Ian (1983). "Noncomputability in analysis and physics: a complete determination of the class of noncomputable linear operators". Advances in Mathematics. 48 (1): 44–74. doi:10.1016/0001-8708(83)90004-X. MR 0697614.
Rogers, Hartley, Jr. (1959). "The present theory of Turing machine computability". Journal of the Society for Industrial and Applied Mathematics. 7: 114–130. doi:10.1137/0107009. MR 0099923.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Kushner, Boris A. (2006). "The constructive mathematics of A. A. Markov". The American Mathematical Monthly. 113 (6): 559–566. doi:10.2307/27641983. JSTOR 27641983. MR 2231143.

archive.org (Global: 6^th place; English: 6^th place)

Minsky (1967). Minsky, Marvin (1967). "9. The Computable Real Numbers". Computation: Finite and Infinite Machines. Prentice-Hall. ISBN 0-13-165563-9. OCLC 0131655639.

arxiv.org (Global: 49^th place; English: 31^st place)

O’Connor, Russell (2008). "Certified Exact Transcendental Real Number Computation in Coq". Theorem Proving in Higher Order Logics. Lecture Notes in Computer Science. Vol. 5170. pp. 246–261. arXiv:0805.2438. doi:10.1007/978-3-540-71067-7_21. ISBN 978-3-540-71065-3. S2CID 17959745.

books.google.com (Global: 3^rd place; English: 3^rd place)

Bridges & Richman (1987), p. 58. Bridges, Douglas; Richman, Fred (1987). Varieties of Constructive Mathematics. Cambridge University Press. ISBN 978-0-521-31802-0.

doi.org (Global: 2^nd place; English: 2^nd place)

van der Hoeven (2006). van der Hoeven, Joris (2006). "Computations with effective real numbers". Theoretical Computer Science. 351 (1): 52–60. doi:10.1016/j.tcs.2005.09.060.
Pour-El, Marian Boykan; Richards, Ian (1983). "Noncomputability in analysis and physics: a complete determination of the class of noncomputable linear operators". Advances in Mathematics. 48 (1): 44–74. doi:10.1016/0001-8708(83)90004-X. MR 0697614.
Rogers, Hartley, Jr. (1959). "The present theory of Turing machine computability". Journal of the Society for Industrial and Applied Mathematics. 7: 114–130. doi:10.1137/0107009. MR 0099923.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Turing (1936). Turing, A. M. (1936). "On Computable Numbers, with an Application to the Entscheidungsproblem". Proceedings of the London Mathematical Society. Series 2. 42 (1) (published 1937): 230–65. doi:10.1112/plms/s2-42.1.230. S2CID 73712.
Turing, A. M. (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction". Proceedings of the London Mathematical Society. Series 2. 43 (6) (published 1937): 544–6. doi:10.1112/plms/s2-43.6.544. Computable numbers (and Turing's a-machines) were introduced in this paper; the definition of computable numbers uses infinite decimal sequences.
Rice (1954). Rice, Henry Gordon (1954). "Recursive real numbers". Proceedings of the American Mathematical Society. 5 (5): 784–791. doi:10.1090/S0002-9939-1954-0063328-5. JSTOR 2031867.
Specker (1949). Specker, E. (1949). "Nicht konstruktiv beweisbare Sätze der Analysis" (PDF). Journal of Symbolic Logic. 14 (3): 145–158. doi:10.2307/2267043. JSTOR 2267043. S2CID 11382421. Archived (PDF) from the original on 2018-07-21.
Hirst (2007). Hirst, Jeffry L. (2007). "Representations of reals in reverse mathematics". Bulletin of the Polish Academy of Sciences, Mathematics. 55 (4): 303–316. doi:10.4064/ba55-4-2.
Kushner, Boris A. (2006). "The constructive mathematics of A. A. Markov". The American Mathematical Monthly. 113 (6): 559–566. doi:10.2307/27641983. JSTOR 27641983. MR 2231143.
Boehm, Hans-J.; Cartwright, Robert; Riggle, Mark; O'Donnell, Michael J. (8 August 1986). "Exact real arithmetic: A case study in higher order programming" (PDF). Proceedings of the 1986 ACM conference on LISP and functional programming - LFP '86. pp. 162–173. doi:10.1145/319838.319860. ISBN 0897912004. S2CID 12934546. Archived (PDF) from the original on 2020-09-24.
O’Connor, Russell (2008). "Certified Exact Transcendental Real Number Computation in Coq". Theorem Proving in Higher Order Logics. Lecture Notes in Computer Science. Vol. 5170. pp. 246–261. arXiv:0805.2438. doi:10.1007/978-3-540-71067-7_21. ISBN 978-3-540-71065-3. S2CID 17959745.
Gowland, Paul; Lester, David (2001). "A Survey of Exact Arithmetic Implementations" (PDF). Computability and Complexity in Analysis. Lecture Notes in Computer Science. Vol. 2064. Springer. pp. 30–47. doi:10.1007/3-540-45335-0_3. ISBN 978-3-540-42197-9. Archived (PDF) from the original on 2022-03-24.

eudml.org (Global: low place; English: low place)

Mazur, Stanisław (1963). Grzegorczyk, Andrzej; Rasiowa, Helena (eds.). Computable analysis. Rozprawy Matematyczne. Vol. 33. Institute of Mathematics of the Polish Academy of Sciences. p. 4.
Hirst (2007). Hirst, Jeffry L. (2007). "Representations of reals in reverse mathematics". Bulletin of the Polish Academy of Sciences, Mathematics. 55 (4): 303–316. doi:10.4064/ba55-4-2.

github.com (Global: 380^th place; English: 337^th place)

Lambov (2015). Lambov, Branimir (5 April 2015). "RealLib". GitHub.

jstor.org (Global: 23^rd place; English: 15^th place)

Rice (1954). Rice, Henry Gordon (1954). "Recursive real numbers". Proceedings of the American Mathematical Society. 5 (5): 784–791. doi:10.1090/S0002-9939-1954-0063328-5. JSTOR 2031867.
Specker (1949). Specker, E. (1949). "Nicht konstruktiv beweisbare Sätze der Analysis" (PDF). Journal of Symbolic Logic. 14 (3): 145–158. doi:10.2307/2267043. JSTOR 2267043. S2CID 11382421. Archived (PDF) from the original on 2018-07-21.
Kushner, Boris A. (2006). "The constructive mathematics of A. A. Markov". The American Mathematical Monthly. 113 (6): 559–566. doi:10.2307/27641983. JSTOR 27641983. MR 2231143.

rero.ch (Global: 3,023^rd place; English: 2,092^nd place)

doc.rero.ch

Specker (1949). Specker, E. (1949). "Nicht konstruktiv beweisbare Sätze der Analysis" (PDF). Journal of Symbolic Logic. 14 (3): 145–158. doi:10.2307/2267043. JSTOR 2267043. S2CID 11382421. Archived (PDF) from the original on 2018-07-21.

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Turing (1936). Turing, A. M. (1936). "On Computable Numbers, with an Application to the Entscheidungsproblem". Proceedings of the London Mathematical Society. Series 2. 42 (1) (published 1937): 230–65. doi:10.1112/plms/s2-42.1.230. S2CID 73712.
Turing, A. M. (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction". Proceedings of the London Mathematical Society. Series 2. 43 (6) (published 1937): 544–6. doi:10.1112/plms/s2-43.6.544. Computable numbers (and Turing's a-machines) were introduced in this paper; the definition of computable numbers uses infinite decimal sequences.
Specker (1949). Specker, E. (1949). "Nicht konstruktiv beweisbare Sätze der Analysis" (PDF). Journal of Symbolic Logic. 14 (3): 145–158. doi:10.2307/2267043. JSTOR 2267043. S2CID 11382421. Archived (PDF) from the original on 2018-07-21.
Boehm, Hans-J.; Cartwright, Robert; Riggle, Mark; O'Donnell, Michael J. (8 August 1986). "Exact real arithmetic: A case study in higher order programming" (PDF). Proceedings of the 1986 ACM conference on LISP and functional programming - LFP '86. pp. 162–173. doi:10.1145/319838.319860. ISBN 0897912004. S2CID 12934546. Archived (PDF) from the original on 2020-09-24.
O’Connor, Russell (2008). "Certified Exact Transcendental Real Number Computation in Coq". Theorem Proving in Higher Order Logics. Lecture Notes in Computer Science. Vol. 5170. pp. 246–261. arXiv:0805.2438. doi:10.1007/978-3-540-71067-7_21. ISBN 978-3-540-71065-3. S2CID 17959745.

springer.com (Global: 182^nd place; English: 172^nd place)

link.springer.com

Gowland, Paul; Lester, David (2001). "A Survey of Exact Arithmetic Implementations" (PDF). Computability and Complexity in Analysis. Lecture Notes in Computer Science. Vol. 2064. Springer. pp. 30–47. doi:10.1007/3-540-45335-0_3. ISBN 978-3-540-42197-9. Archived (PDF) from the original on 2022-03-24.

uni.wroc.pl (Global: 8,573^rd place; English: low place)

fricas-wiki.math.uni.wroc.pl

Boehm, Hans-J.; Cartwright, Robert; Riggle, Mark; O'Donnell, Michael J. (8 August 1986). "Exact real arithmetic: A case study in higher order programming" (PDF). Proceedings of the 1986 ACM conference on LISP and functional programming - LFP '86. pp. 162–173. doi:10.1145/319838.319860. ISBN 0897912004. S2CID 12934546. Archived (PDF) from the original on 2020-09-24.

web.archive.org (Global: 1^st place; English: 1^st place)

Specker (1949). Specker, E. (1949). "Nicht konstruktiv beweisbare Sätze der Analysis" (PDF). Journal of Symbolic Logic. 14 (3): 145–158. doi:10.2307/2267043. JSTOR 2267043. S2CID 11382421. Archived (PDF) from the original on 2018-07-21.
Boehm, Hans-J.; Cartwright, Robert; Riggle, Mark; O'Donnell, Michael J. (8 August 1986). "Exact real arithmetic: A case study in higher order programming" (PDF). Proceedings of the 1986 ACM conference on LISP and functional programming - LFP '86. pp. 162–173. doi:10.1145/319838.319860. ISBN 0897912004. S2CID 12934546. Archived (PDF) from the original on 2020-09-24.
Gowland, Paul; Lester, David (2001). "A Survey of Exact Arithmetic Implementations" (PDF). Computability and Complexity in Analysis. Lecture Notes in Computer Science. Vol. 2064. Springer. pp. 30–47. doi:10.1007/3-540-45335-0_3. ISBN 978-3-540-42197-9. Archived (PDF) from the original on 2022-03-24.

worldcat.org (Global: 4^th place; English: 4^th place)

search.worldcat.org

Minsky (1967). Minsky, Marvin (1967). "9. The Computable Real Numbers". Computation: Finite and Infinite Machines. Prentice-Hall. ISBN 0-13-165563-9. OCLC 0131655639.

Computable number (English Wikipedia)

abelard.org (Global: low place; English: low place)

ams.org (Global: 434th place; English: 249th place)

mathscinet.ams.org

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 49th place; English: 31st place)

books.google.com (Global: 3rd place; English: 3rd place)

doi.org (Global: 2nd place; English: 2nd place)

eudml.org (Global: low place; English: low place)

github.com (Global: 380th place; English: 337th place)

jstor.org (Global: 23rd place; English: 15th place)

rero.ch (Global: 3,023rd place; English: 2,092nd place)

doc.rero.ch

semanticscholar.org (Global: 15th place; English: 8th place)

api.semanticscholar.org

springer.com (Global: 182nd place; English: 172nd place)

link.springer.com

uni.wroc.pl (Global: 8,573rd place; English: low place)

fricas-wiki.math.uni.wroc.pl

web.archive.org (Global: 1st place; English: 1st place)

worldcat.org (Global: 4th place; English: 4th place)

search.worldcat.org

ams.org (Global: 434^th place; English: 249^th place)

archive.org (Global: 6^th place; English: 6^th place)

arxiv.org (Global: 49^th place; English: 31^st place)

books.google.com (Global: 3^rd place; English: 3^rd place)

doi.org (Global: 2^nd place; English: 2^nd place)

github.com (Global: 380^th place; English: 337^th place)

jstor.org (Global: 23^rd place; English: 15^th place)

rero.ch (Global: 3,023^rd place; English: 2,092^nd place)

semanticscholar.org (Global: 15^th place; English: 8^th place)

springer.com (Global: 182^nd place; English: 172^nd place)

uni.wroc.pl (Global: 8,573^rd place; English: low place)

web.archive.org (Global: 1^st place; English: 1^st place)

worldcat.org (Global: 4^th place; English: 4^th place)