Abstract
Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms.Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.
Original language | English |
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Pages (from-to) | 1-30 |
Number of pages | 30 |
Journal | Foundations of Science |
Early online date | 24 Jun 2017 |
DOIs | |
Publication status | Published - 2017 |
Keywords
- Cauchy’s infinitesimal
- Foundational paradigms
- Quantifier alternation
- Sum theorem
- Uniform convergence