bib.bib

@article{richards,
 ISSN = {0025570X, 19300980},
 URL = {http://www.jstor.org/stable/2689627},
 author = {Ian Richards},
 journal = {Mathematics Magazine},
 number = {4},
 pages = {163--171},
 publisher = {Mathematical Association of America},
 title = {Continued Fractions without Tears},
 volume = {54},
 year = {1981}
}

@article{ittay-2015,
 ISSN = {00357596, 19453795},
 URL = {https://www.jstor.org/stable/26411448},
 abstract = {We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts to recent results, and allowing for a simple comparison-at-a-glance between different constructions.},
 author = {Ittay Weiss},
 journal = {The Rocky Mountain Journal of Mathematics},
 number = {3},
 pages = {737--762},
 publisher = {Rocky Mountain Mathematics Consortium},
 title = {Survey Article: The Real Numbers--A Survey of Constructions},
 volume = {45},
 year = {2015},
       eprint={1503.04348},
      archivePrefix={arXiv},
      primaryClass={math.HO}
}

@unpublished{weiss2015reals,
      title={The reals as rational Cauchy filters}, 
      author={Ittay Weiss},
      year={2015},
    note={on Arxiv},
      eprint={1503.04348},
      archivePrefix={arXiv},
      primaryClass={math.HO}
}


@article{BBP,
    author = "David Bailey and Peter Borwein and Simon Plouffe",
    title = "On the rapid computation of various polylogarithmic constants",
    journal = "Mathematics of Computation",
    volume = "66",
    pages = "903--913",
    year = "1997",
    DOI =  "https://doi.org/10.1090/S0025-5718-97-00856-9"
}

@article{mend,
 ISSN = {00029890, 19300972},
 URL = {http://www.jstor.org/stable/2306324},
 author = {N. S. Mendelsohn},
 journal = {The American Mathematical Monthly},
 number = {8},
 pages = {563--563},
 publisher = {Mathematical Association of America},
 title = {An Application of a Famous Inequality},
 volume = {58},
 year = {1951}
}

@COMMENT { BibTex package created from National Library of Australia Catalogue https://catalogue.nla.gov.au  }
@Book{ rudin,
author = { Rudin, Walter },
title = { Principles of mathematical analysis },
edition = { 3d ed. },
publisher = { McGraw-Hill New York },
pages = { x, 342 p. ; },
year = { 1976 },
type = { Book },
language = { English },
subjects = { Mathematical analysis. },
life-dates = { 1976 - 2010  }
}

 @book{bridges, place={New York}, title={Techniques of constructive analysis}, publisher={Springer}, author={Bridges, D. S. and Vita, Luminita Simona}, year={2006}} 

 @book{bridger, title={Real analysis: A constructive approach}, publisher={John Wiley \& Sons}, author={Bridger, Mark}, year={2006}} 

@article{BriStol,
 ISSN = {00029890, 19300972},
 URL = {http://www.jstor.org/stable/2589492},
 author = {Mark Bridger and Gabriel Stolzenberg},
 journal = {The American Mathematical Monthly},
 number = {7},
 pages = {628--635},
 publisher = {Mathematical Association of America},
 title = {Uniform Calculus and the Law of Bounded Change},
 urldate = {2023-01-30},
 volume = {106},
 year = {1999}
}

@article{fowler,
author = {David Fowler},
title = {Dedekind's Theorem },
journal = {The American Mathematical Monthly},
volume = {99},
number = {8},
pages = {725-733},
year  = {1992},
publisher = {Taylor & Francis},
doi = {10.1080/00029890.1992.11995919},

}


@book{maudlin,
    author = {Maudlin, Tim},
    title = {New Foundations for Physical Geometry: The Theory of Linear Structures},
    publisher = {Oxford University Press},
    year = {2014},
    month = {03},
    abstract = "{Topology is the mathematical study of the most basic geometrical structure of a space. Mathematical physics uses topological spaces as the formal means for describing physical space and time. This book proposes a completely new mathematical structure for describing geometrical notions such as continuity, connectedness, boundaries of sets, and so on, in order to provide a better mathematical tool for understanding space-time. This is the initial volume in a two-volume set, the first of which develops the mathematical structure and the second of which applies it to classical and Relativistic physics. The book begins with a brief historical review of the development of mathematics as it relates to geometry, and an overview of standard topology. The new theory, the Theory of Linear Structures, is presented and compared to standard topology. The Theory of Linear Structures replaces the foundational notion of standard topology, the open set, with the notion of a continuous line. Axioms for the Theory of Linear Structures are laid down, and definitions of other geometrical notions developed in those terms. Various novel geometrical properties, such as a space being intrinsically directed, are defined using these resources. Applications of the theory to discrete spaces (where the standard theory of open sets gets little purchase) are particularly noted. The mathematics is developed up through homotopy theory and compactness, along with ways to represent both affine (straight line) and metrical structure.}",
    isbn = {9780198701309}
}


@book{moore,
   title =     {Introduction To Interval Analysis},
   author =    {Moore, Ramon E. and R. Baker Kearfott, Michael J. Cloud},
   publisher = {Society for Industrial and Applied Mathematics},
   isbn =      {9780898716696},
   year =      {2009},
   edition =   {1},
}



@article{shiu95,
 ISSN = {00255718, 10886842},
 URL = {http://www.jstor.org/stable/2153497},
 abstract = {An algorithm for the computation of the continued fraction expansions of numbers which are zeros of differentiable functions is given. The method is direct in the sense that it requires function evaluations at appropriate steps, rather than the value of the number as input in order to deliver the expansion. Statistical data on the first 10000 partial quotients for various real numbers are also given.},
 author = {P. Shiu},
 journal = {Mathematics of Computation},
 number = {211},
 pages = {1307--1317},
 publisher = {American Mathematical Society},
 title = {Computation of Continued Fractions Without Input Values},
 volume = {64},
 year = {1995}
}

@unpublished{taylor23main, 
    title={Defining Real Numbers as Oracles},
    author={James Taylor},
    note={Drafted},
      eprint={2305.04935},
      archivePrefix={arXiv},
      primaryClass={math.GM},
    URL={https://github.com/jostylr/Reals-as-Oracles},
    year={2023}
}

@unpublished{taylor23teaser,
      title={Rationally Querying the Reals}, 
      author={James Taylor},
      year={2023},
      note={Drafted, 4 pages},
      eprint={2305.00981},
      archivePrefix={arXiv},
      primaryClass={math.GM},
    URL={https://github.com/jostylr/Reals-as-Oracles},
}

@unpublished{taylor23over,
      title={Defining Real Numbers as Oracles, an Overview}, 
      author={James Taylor},
      year={2023},
      note={Drafted, 20 pages. Not separately on arXiv as arXiv does not want similar work.},
      eprint={2305.04935v1},
      archivePrefix={arXiv},
      primaryClass={math.GM},
      URL={https://github.com/jostylr/Reals-as-Oracles},
}

@unpublished{taylor23metric, 
    title={Topological Completions with Oracles},
    author={James Taylor},
    note={Under development},
    URL={https://github.com/jostylr/Reals-as-Oracles},
    year={2023}
}

@unpublished{taylor23maudlin, 
    title={Linear Structures and Oracles},
    author={James Taylor},
    note={Under development},
    URL={https://github.com/jostylr/Reals-as-Oracles},
    year={2023}
}

@unpublished{taylor23funora, 
    title={Elementary Analysis with Function Oracles},
    author={James Taylor},
    note={Under development},
    URL={https://github.com/jostylr/Reals-as-Oracles},
    year={2023}
}


@unpublished{taylor23edu, 
    title={Rational Mathematics Education},
    author={James Taylor},
    note={Under development},
    URL={https://github.com/jostylr/Reals-as-Oracles},
    year={2023}
}

@unpublished{taylor24dedekind, 
    title={Rational Betweenness Relations From Dedekind Cuts},
    author={James Taylor},
    note={Under development},
    URL={https://github.com/jostylr/Reals-as-Oracles},
    year={2024}
}

@unpublished{taylor24oraclerbr, 
    title={Real Numbers As Rational Betweenness Relations},
    author={James Taylor},
    note={Under development},
    URL={https://github.com/jostylr/Reals-as-Oracles},
    year={2024}
}


@article{samuel,
 ISSN = {00029947},
 URL = {http://www.jstor.org/stable/1990559},
 author = {Pierre Samuel},
 journal = {Transactions of the American Mathematical Society},
 number = {1},
 pages = {100--132},
 publisher = {American Mathematical Society},
 title = {Ultrafilters and Compactification of Uniform Spaces},
 urldate = {2023-07-12},
 volume = {64},
 year = {1948}
}


@book{hubbard,
  title={Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach (5th edition)},
  author={John H. Hubbard and Barbara Burke Hubbard},
  year={2015},
    publisher = {Matrix Editions},
  url={https://matrixeditions.com/5thUnifiedApproach.html}
}



@article{propp,
author = {James Propp},
title = {Real Analysis in Reverse},
journal = {The American Mathematical Monthly},
volume = {120},
number = {5},
pages = {392-408},
year = {2013},
publisher = {Taylor & Francis},
doi = {10.4169/amer.math.monthly.120.05.392},
URL = { 
        https://www.tandfonline.com/doi/abs/10.4169/amer.math.monthly.120.05.392
},
eprint = {         https://www.tandfonline.com/doi/pdf/10.4169/amer.math.monthly.120.05.392}
}