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==References== {{refbegin|30em}} *{{cite book |first1=Douglas |last1=Bridges |first2=Fred |last2=Richman |title=Varieties of Constructive Mathematics |url=https://books.google.com/books?id=oN5nsPkXhhsC |date=1987 |publisher=Cambridge University Press |isbn=978-0-521-31802-0 }} *{{cite journal |first=Jeffry L. |last=Hirst |title=Representations of reals in reverse mathematics |journal= Bulletin of the Polish Academy of Sciences, Mathematics|year=2007 |volume=55 |issue=4 |pages=303β316 |url=https://eudml.org/doc/281227 |doi=10.4064/ba55-4-2|doi-access=free }} *{{Cite web |title=RealLib |last=Lambov |first=Branimir |publisher=GitHub |date=5 April 2015 |url= https://github.com/blambov/RealLib }} *{{cite book |author-link=Marvin Minsky |first=Marvin |last=Minsky |chapter=9. The Computable Real Numbers |title=Computation: Finite and Infinite Machines |url=https://archive.org/details/computationfinit0000mins |url-access=registration |publisher=Prentice-Hall |year=1967 |isbn=0-13-165563-9 |oclc=0131655639}} *{{cite journal |first=Henry Gordon |last=Rice |title=Recursive real numbers |journal=Proceedings of the American Mathematical Society |year=1954 |volume=5 |issue=5 |pages=784β791 |doi=10.1090/S0002-9939-1954-0063328-5 |jstor=2031867 |doi-access=free }} *{{cite journal |first=E. |last=Specker |author-link = Ernst Specker|title=Nicht konstruktiv beweisbare SΓ€tze der Analysis |journal=Journal of Symbolic Logic |year=1949 |volume=14 |issue=3 |pages=145β158 |doi=10.2307/2267043 |jstor=2267043|s2cid=11382421 |url=http://doc.rero.ch/record/304204/files/S0022481200105663.pdf |archive-url=https://web.archive.org/web/20180721231142/http://doc.rero.ch/record/304204/files/S0022481200105663.pdf |archive-date=2018-07-21 |url-status=live }} *{{cite journal | last= Turing | first= A. M. | publication-date = 1937 | year = 1936 | title = On Computable Numbers, with an Application to the Entscheidungsproblem | periodical = Proceedings of the London Mathematical Society | series = Series 2 | volume = 42 | issue= 1 | pages = 230β65 | doi= 10.1112/plms/s2-42.1.230 | s2cid= 73712 }}<br/>{{cite journal | last = Turing | first = A. M. | publication-date = 1937 | title = On Computable Numbers, with an Application to the Entscheidungsproblem: A correction | periodical = Proceedings of the London Mathematical Society | series = Series 2 | volume = 43 | issue = 6 | pages = 544β6 | url = http://www.abelard.org/turpap2/tp2-ie.asp | doi = 10.1112/plms/s2-43.6.544 | year = 1938 }} Computable numbers (and Turing's a-machines) were introduced in this paper; the definition of computable numbers uses infinite decimal sequences. *{{cite journal |last1=van der Hoeven |first1=Joris |title=Computations with effective real numbers |journal=Theoretical Computer Science |date=2006 |volume=351 |issue=1 |pages=52β60 |doi=10.1016/j.tcs.2005.09.060|doi-access=free }} {{refend}}
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