Around Bolzano's approach to real numbers

Djuro R. Kurepa

Czechoslovak Mathematical Journal (1982)

  • Volume: 32, Issue: 4, page 655-666
  • ISSN: 0011-4642

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Kurepa, Djuro R.. "Around Bolzano's approach to real numbers." Czechoslovak Mathematical Journal 32.4 (1982): 655-666. <http://eudml.org/doc/13352>.

@article{Kurepa1982,
author = {Kurepa, Djuro R.},
journal = {Czechoslovak Mathematical Journal},
keywords = {foundations of real analysis; constructive mathematics; intermediate value theorem; Dedekind; Cantor; nonstandard analysis},
language = {eng},
number = {4},
pages = {655-666},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Around Bolzano's approach to real numbers},
url = {http://eudml.org/doc/13352},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Kurepa, Djuro R.
TI - Around Bolzano's approach to real numbers
JO - Czechoslovak Mathematical Journal
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 4
SP - 655
EP - 666
LA - eng
KW - foundations of real analysis; constructive mathematics; intermediate value theorem; Dedekind; Cantor; nonstandard analysis
UR - http://eudml.org/doc/13352
ER -

References

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  2. Bolzano Bernard, Rein analytischer Beweis des Lehrsatzes, dass zwischen je zwey Werthen, die ein entgegensetztes Resultat gewähren, wenigstens eine reelle Wurzel der Gleichung liege, Abhandlungen der Kgl. Ges. der Wiss. Prag 1817, pp. 1 - 60 (photocopy pp. 417-476 in Bolzano (1981)). (1981) 
  3. Bolzano Bernard, Funktionenlehre in: Spisy Bernarda Bolzana - Bernard Bolzano's Schriften I, herausgegeben u. mit Anmerkungen versehen von K. Rychlik. Prag 1930, XX - 183 (written by В. Bolzano in the period 1833-1841) + 24 + VI. (1930) 
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  5. Cantor Georg, 10.1007/BF01446327, Math. Ann 5 (1872) pp. 123-132 = pp. 92-101 in Georg Cantor, Gesammelte Abhandlungen. 1966 Hildesheim, pp. VII + 486; cf. also pp. 183-190 (§ 9). (1966) MR1509769DOI10.1007/BF01446327
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  7. Dedekind Richard, Stetigkeit und irrationale Zahlen, Braunschweig 1872; pp. 315-334 in Richard Dedekind, Gesammelte Schriften 3, Braunschweig 1932, pp. 4 + 508. (1932) MR0114755
  8. Dhombres Jean, Nombre, mesure et continu. Epistomologie et histoire, Ed. Cedic/Fernand Nathan, Paris 1978, pp. 339. (1978) Zbl0412.01001
  9. Fowler D. H., 10.1090/S0273-0979-1979-14684-6, Bull. Amer. Math. Soc. N.S. 1 : 6 (1979), 807-846. (1979) Zbl0425.01002MR0546311DOI10.1090/S0273-0979-1979-14684-6
  10. Jarník Vojtěch, Bolzano and the foundations of mathematical analysis, Preface by J. Novák; Introductory article 11 - 31 by J. Folta, translation: J. Jarník, J.Č.M.F., Praha 1981, pp. 1-90. (1981) 
  11. Knopp Konrad, Theorie und Anwendung der unendlichen Reihen 1924 2 , Grundlehren der math. Wiss. Bd 2 (Berlin 1924) X + 528. (First edition 1922, Berlin: J. Springer X + 474, V. J. Fortschritte d. Math. 48 (1921-22) pp. 222-23). (1924) Zbl48.0222.01MR0028430
  12. Kolmogorov A. N., K obosnovaniju teorii vescestvennyh cisel, (On the foundation of the theory of real numbers) Uspehi Mat. Nauk 1 (11) (1946) 217-219. Časopis pěst. mat. 76 (1951) 155-157. M. R. 14 (1953) 255. (1946) MR0049974
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  14. Kurepa Duro, History of irrational numbers, Lectured in Zagreb May 8, 1928 (unpublished). (1928) 
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