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HandWiki. Criticism of Non-Standard Analysis. Encyclopedia. Available online: https://encyclopedia.pub/entry/32987 (accessed on 24 September 2026).
HandWiki. Criticism of Non-Standard Analysis. Encyclopedia. Available at: https://encyclopedia.pub/entry/32987. Accessed September 24, 2026.
HandWiki. "Criticism of Non-Standard Analysis" Encyclopedia, https://encyclopedia.pub/entry/32987 (accessed September 24, 2026).
HandWiki. (2022, November 04). Criticism of Non-Standard Analysis. In Encyclopedia. https://encyclopedia.pub/entry/32987
HandWiki. "Criticism of Non-Standard Analysis." Encyclopedia. Web. 04 November, 2022.
Criticism of Non-Standard Analysis
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The content is sourced from: https://handwiki.org/wiki/Criticism_of_non-standard_analysis

Non-standard analysis and its offshoot, non-standard calculus, have been criticized by several authors, notably Errett Bishop, Paul Halmos, and Alain Connes. These criticisms are analyzed below.

analysis calculus non-standard

References

  1. Tao, T.: Structure and randomness. Pages from year one of a mathematical blog. American Mathematical Society, Providence, RI, 2008. p. 55.
  2. This is shown in Edward Nelson's AMS 1977 paper in an appendix written by William Powell.
  3. Diane., Ravitch (2000). Left back : a century of failed school reforms. New York: Simon & Schuster. ISBN 0684844176. OCLC 43790988. https://archive.org/details/leftbackcenturyo00ravi_0. 
  4. Philip, J. Davis (April 9, 2001). "SIAM: Educational Enthusiasms and Their Critics". https://archive.siam.org/news/news.php?id=527. 
  5. in Donald Gillies, Revolutions in Mathematics (1992), p. 76.
  6. Bishop, Errett (1975). "The crisis in contemporary mathematics" (in en). Historia Mathematica 2 (4): 507–517. doi:10.1016/0315-0860(75)90113-5.  https://dx.doi.org/10.1016%2F0315-0860%2875%2990113-5
  7. Stolzenberg 1978.
  8. See Katz & Katz (2011)
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