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What is 0^0? - Conclusion and Bibliography

Michael Huber and V. Frederick Rickey


In keeping with the honored pedagogical technique of "First tell 'em what you are going to tell 'em, then tell 'em, then tell 'em what you told 'em," we summarize. If you are dealing with limits, then 00 is an indeterminate form, but if you are dealing with ordinary algebra, then 00 = 1.




  1. George Baron, "A short Disquisition, concerning the Definition, of the word Power, in Arithmetic and Algebra," The Mathematical Correspondent (1804), pages 59 - 66. Available here (pdf download) and from Google Books beginning here.
  2. Augustin-Louis Cauchy, Cours d'Analyse de l'Ecole Royale Polytechnique (1821). In his Oeuvres Complètes, series 2, volume 3, available here from Gallica Digital Library.
  3. William Emerson, A treatise of algebra, in two books, 2nd edition, J. Nourse, London, 1780. Title page and pages 208-213, including the problem "To explain the several properties of (0) nothing, and infinity," available here (pdf download), courtesy of United States Military Academy Library.
  4. Leonhard Euler, Elements of Algebra, translated by Rev. John Hewlett, Springer-Verlag, New York, 1984, pages 50 - 51.
  5. Leonhard Euler, Introduction to Analysis of the Infinite, translated by John D. Blanton, Springer-Verlag, New York, 1988, pages 75 - 76.
  6. E. Keenan, A. X. Gantert, and I. Dressler, Mathematics B, Amsco School Publications, Inc., New York, 2002.
  7. Donald Knuth, "Two Notes on Notation," The American Mathematical Monthly, Volume 99, Number 5, May 1992, pages 403 - 422. This is available in JSTOR.
  8. Guillaume Libri, "Mèmoire sur les functions discontinues," Journal für die reine und angewandte Mathematik, 10 (1833), pages 303 - 316. Available here (pdf download), courtesy of Göttingen State and University Library Digitalization Center (GDZ).
  9. Jared Mansfield, Essays, mathematical and physical: containing new theories and illustrations of some very important and difficult subjects of the sciences, W. W. Morse, New Haven, 1802. Title page and pages 12-17, including first five pages of the essay "Of Nothing and Infinity," available here (pdf download), courtesy of United States Military Academy Library.
  10. Herbert E. Vaughan, "The Expression of 00," The Mathematics Teacher, Volume 63, February 1970, page 111.


Editor's note: This article was published in March of 2008.

Michael Huber and V. Frederick Rickey, "What is 0^0? - Conclusion and Bibliography," Convergence (July 2012)