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Mathematical rigor is like clothing; in its style it ought to suit the occasion, and it diminishes comfort and restrains freedom of movement if it is either too loose or too tight. In The Mathematical Intelligencer, v. 13, no. 1, Winter 1991. |
Loci: ConvergenceAn Analysis of the First Proofs of the Heine-Borel TheoremWorks Cited1. Bloch, E. (2011). The real numbers and real analysis. New York: Springer. 2. Borel, É. (1903). Contribution à l’analyse arithmétique du continu. Journal de mathématiques pures et appliquées 5e série, 329-375. 3. Borel, É. (1898). Leçons sur la théorie des fonctions. Paris: Gauthier-Villars. 4. Borel, É. (1903). Sur l'approximation des nombres par des nombres rationnels. Comptes Rendus de l'Académie des Sciences de Paris, 1054-1055. 5. Borel, É. (1895). Sur quelques points de la théorie des fonctions. Annales scientifiques de l'E.N.S. Serie 3, 12, 9-55. 6. Bressoud, D. M. (2008). A radical approach to Lebesgue's theory of integration. New York: Cambridge University Press. 7. Cousin, P. (1895). Sur les fonctions de n variables complexes. Acta Mathematica, 19, 22. 8. Dugac, P. (1989). Sur la correspondance de Borel et le théorème de Dirichlet-Heine-Weierestrass-Borel-Schoenflies-Lebesgue. Archives internationales d'histoire des sciences, 39 (122), 69-110. 9. Hallett, M. (1979). Towards a theory of mathematical research programmes (I). The British Journal for the Philosophy of Science, 30 (1), 1-25. 10. Hawkins, T. (1980). The origins of modern theories of integration. In I. Grattan-Guinness, From the calculus to set theory 1630-1910, an introductory history (p. 175). Princeton: Princeton University Press. 11. Hildebrandt, T. (1926). The Borel theorem and its generalizations. Bulletin of the American Mathematical Society, 423-425. 12. Koetsier, T. and J. van Mill (1999). By their fruits ye shall know them: some remarks on the interaction of general topology with other areas of mathematics. In History of Topology (pp. 199-239). Amsterdam: North-Holland Publishing Company. 13. Lebesgue, H. (1907). Comptes rendus et analyses: Review of Young and Young, The theory of sets of points. Bulletin des sciences mathématiques (2), 31, 132-134. 14. Lebesgue, H. (1904). Leçons sur l'intégration et la recherche des fonctions primitives. Paris. 15. Schoenflies, A. (1900). Die Entwickelung der Lehre von den Punktmannigfaltigkeiten. In Jahresbericht der deutschen Mathematiker-Vereinigung. Leipzig: B.G. Teubner. Also available from Google Books. 16. Schoenflies, A. (1907). Sur un théorème de Heine et un théorème de Borel. Comptes Rendus de l'Académie des Sciences de Paris, 144, 22-23. 17. Stoll, R. R. (1979). Set Theory and Logic. New York, New York, USA: Dover. 18. Sundström, M. R. (2010 21-June). A pedagogical history of compactness. 19. Young, W. H. (1902). Overlapping intervals. Bulletin of the London Mathematical Society, 35, 384-388.
Pages: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Andre, Nicole R., Susannah M. Engdahl and Adam E. Parker, "An Analysis of the First Proofs of the Heine-Borel Theorem," Loci (July 2012), DOI: 10.4169/loci003890 |