Analysis in the Computable Number Field

  title={Analysis in the Computable Number Field},
  author={Oliver Aberth},
  journal={J. ACM},
  • O. Aberth
  • Published 1 April 1968
  • Mathematics, Computer Science
  • J. ACM
It is well known that real variable analysis is nonconstructive. For example, although it is asserted that every bounded monotone sequence converges to a limit, there is no algorithm for obtaining this limit. This paper presents a constructive analysis which is restricted to a countable set of numbers, the field of computable numbers. These numbers are defined in a new way by employing the concept of “programmable functions.” The resultant analysis differs from real analysis in many important… 
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  • Olivier Sudac
  • Computer Science, Mathematics
    Theor. Comput. Sci.
  • 2001
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  • 1973
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  • O. Aberth
  • Computer Science
    J. Comput. Syst. Sci.
  • 1971
A classification of computational problems is proposed which may have applications in numerical analysis. The classification utilizes the concept of effective method, which has been employed in
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  • J. Myhill
  • Mathematics, Computer Science
    J. Symb. Log.
  • 1953
The purpose of this paper is to prove two theorems and a conjecture (Conjecture II) announced in section 15 an earlier paper of the author's (cited as “ CT ”), and to compare them briefly with
Nicht Konstruktiv Beweisbare Satze Der Analysis
  • E. Specker
  • Mathematics, Computer Science
    J. Symb. Log.
  • 1949
Nach allgemeiner Ueberzeugung konnen gewisse Satze der Analysis nicht konstruktiv bewiesen werden.
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  • 1961
Recursive Analysis. North-II
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  • 1961
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  • 1959
On computable numbers , with au application to the Entseheidungs prob
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  • 1959
Comp~tability and Un,~olvability. Me(ir,.tw-Hill
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  • 1958
On constructive functions
  • Trudy Mat. Inst. b,~. Steklova
  • 1958