Quasi−Ⅽauⅽhy sequenⅽe

Document Type : Translation Paper

Authors

1 University of Kashan

2 Shahid Beheshti University

Abstract

This paper is a translation of the the following paper into Persian:
[Ⅾaviⅾ Burton anⅾ John Ⅽoⅼeⅿan، Quasi−Ⅽauⅽhy Sequenⅽe، Aⅿer. Ⅿath. Ⅿonthⅼy, 117 no. 4 (2010) 328-333.]
 
Beginning students often misunderstand the definition of Cauchy sequences when they first encounter it in an introductory real analysis course. In particular, many students fail to understand that it involves far more than that the distance between successive terms is tending to zero. Nevertheless, sequences which satisfy this weaker property are interesting in their own right. We call them quasi-Cauchy.

References

[1] S. Bosch, U. Guntzer and R. Remmert, Non-Archimedean Analysis, 261, Springer-Verlag, Berlin, 1984.
[2] J. P. Coleman, Nonexpansive algebras, Algebra Universalis, 55 (2006) 479–494.
[3] J. de Groot, Non-Archimedean metrics in topology, Proc. Amer. Math. Soc., 7 (1956) 948–956.
[4] A. J. Lemin, Proximity on isosceles spaces, Russian Math. Surveys, 39 (1984) 143–144.
[5] S. Priess-Crampe and P. Ribenboim, Ultrametric spaces and logic programming, J. Logic Programming, 42 (2000) 59–70.
Mathematics and Society
Volume 2, Issue 2
June 2017
Pages 35-41

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History

  • Receive Date: 10 December 2015
  • Revise Date: 28 May 2016
  • Accept Date: 17 July 2016
  • Publish Date: 23 August 2017

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