References for: The real numbers: Stevin to Hilbert


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Books:
  1. J N Crossley, The emergence of number (Upside Down A Book Company, Yarra Glen, 1980).
  2. J V Grabiner, The origins of Cauchy's rigorous calculus (The MIT Press, Cambridge, Massachusetts, 1981).
  3. H N Jahnke (ed.), A history of analysis (American Mathematical Society, Providence, R.I., 2003).
  4. C J Scriba, The concept of number (Mannheim-Zurich, 1968).
Papers:
  1. V S Albis González, and L I Soriano-Lleras, The work of Indalecio Liévano on the foundations of real numbers, Historia Math. 3 (2) (1976), 161-166.
  2. J-P Belna, Les nombres réels : Frege critique de Cantor et de Dedekind, Rev. Histoire Sci. 50 (1-2) (1997), 131-158.
  3. R P Burn, Irrational numbers in English language textbooks, 1890-1915 : constructions and postulates for the completeness of the real numbers, Historia Math. 19 (2) (1992), 158-176.
  4. J R Chicano Requena, The founding of analysis in the nineteenth century: a model for the real numbers (Catalan), Butl. Soc. Catalana Mat. No. 5 (1990), 67-73.
  5. R P Coelho, Old and new aspects of the theory of real numbers. I (Portuguese), in Proceedings of the First Spanish- Portuguese Mathematical Conference, Madrid, 1973, Consejo Sup. Inv. Cient. (Madrid, 1977), 168-181.
  6. J N Crossley, Number. I. Irrational numbers. Part 1, Austral. Math. Soc. Gaz. 4 (3) (1977), 73-85.
  7. J N Crossley, Number. I. Irrational numbers. Part 2, Austral. Math. Soc. Gaz. 5 (1) (1978), 1-14.
  8. J J da Silva, Wittgenstein on irrational numbers, in Wittgenstein's philosophy of mathematics, Kirchberg am Wechsel, 1992 (Hölder-Pichler-Tempsky, Vienna, 1993), 93--99.
  9. J G Dhombres, Real numbers from Cauchy to Robinson, Southeast Asian Bull. Math. 1 (1) (1977), 9-20.
  10. P Djugak, The limit concept and irrational numbers: ideas of Charles Méray and Karl Weierstrass (Russian), inStudies in the history of mathematics, No. 18 (Russian), (Izdat. "Nauka", Moscow, 1973), 176-180; 338.
  11. S Giuntini, A discussion concerning the nature of zero and the relation between imaginary and real numbers (Italian), Boll. Storia Sci. Mat. 4 (1) (1984), 25-63.
  12. M Lopez Pellicer, Constructions of real numbers (Spanish), in History of mathematics in the XIXth century, Part 2 (Spanish), Madrid, 1993, Real Acad. Cienc. Exact. Fís. Natur. (Madrid, 1994), 11-33.
  13. A I Markusevic, Remarks on the paper: "Cantor's theory of real numbers" by F A Medvedev (Russian), Istor.-Mat. Issled. No. 23 (1978), 71-76; 357.
  14. F A Medvedev, Cantor's theory of real numbers (Russian), Istor.-Mat. Issled. No. 23 (1978), 56-70; 357.
  15. F A Medvedev, On the problem of completeness in the theories of real numbers (Russian), Voprosy Istor. Estestvoznan. i Tekhn. (1) (1981), 106-107.
  16. L C Mejlbo, Addendum to: "Some fundamental theorems about real numbers and their history" (Danish), Nordisk Mat. Tidskr. 25/26 (3-4) (1978), 120; 208.
  17. L C Mejlbo, Some fundamental theorems about real numbers and their history (Danish), Nordisk Mat. Tidskr. 25/26 (2) (1978), 57-69; 111.
  18. K Rychlik, Theory of real numbers in the manuscripts left by Bolzano (Czech), Casopis Pest. Mat. 81 (1956), 391-395.
  19. P M Simons, Frege's theory of real numbers, Hist. Philos. Logic 8 (1) (1987), 25-44.
  20. P M Simons, Frege's theory of real numbers, in Frege's philosophy of mathematics (Harvard Univ. Press, Cambridge, MA, 1995), 358-385.
  21. J Simsa, Development of the concept of real numbers (Czech), in Mathematics in the 16th and 17th centuries (Czech), Jevícko, 1997 (Prometheus, Prague, 1999), 259-282.
  22. F Smithies, Weierstrass's theory of the real numbers, Bull. Inst. Math. Appl. 11 (1-2) (1975), 24-27.
  23. J E Snow, Views on the real numbers and the continuum, Rev. Mod. Log. 9 (1-2) 2001/03), 95-113.
  24. B van Rootselaar, Bolzano's theory of real numbers, Arch. History Exact Sci. 2 (1964/1965), 168-180.

JOC/EFR October 2005

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