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Convergence of Numerical Sequences – a Commentary on “the Vice: Some Historically Inspired and Proof Generated Steps to Limits of Sequences” By R.P. Burn

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Abstract

Burn (2005) proposes a genetic approach to teaching limits of numerical sequences. The article includes an explanation of the Method of Exhaustion,1 a generalization of this method, and a description of how this method was used for obtaining areas and lengths in the seventeenth century. The author uses these historical and mathematical analyses as a basis for proposing an alternative definition of the limit of a sequence. The paper focuses on the fine mathematical and historical detail of the notion of limit. Reading it made me reflect on the explicitly or implicitly involved didactical aspects, which I would like to share with ESM readers.

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Authors and Affiliations

  1. Concordia University Department of Mathematics and Statistics, 7141 Sherbrooke Street West, H4B 1R6, Montreal, Quebec, Canada

    Analía Bergé

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  1. Analía Bergé
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Correspondence to Analía Bergé.

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This paper was published in ESM 60.3, 2005.

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Bergé, A. Convergence of Numerical Sequences – a Commentary on “the Vice: Some Historically Inspired and Proof Generated Steps to Limits of Sequences” By R.P. Burn. Educ Stud Math 61, 395–402 (2006). https://doi.org/10.1007/s10649-006-8754-9

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  • DOI: https://doi.org/10.1007/s10649-006-8754-9

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