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The notion of variable quantities ω in Bolzano’s early works
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SYSNO ASEP 0535527 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The notion of variable quantities ω in Bolzano’s early works Author(s) Fuentes Guillén, Elías (FLU-F) ORCID, RID, SAI
Martínez Adame, C. (MX)Source Title Historia Mathematica. - : Elsevier - ISSN 0315-0860
-, č. 50 (2020), s. 25-49Number of pages 25 s. Publication form Print - P Language eng - English Country US - United States Keywords History of nineteenth century ; mathematics ; Bolzano ; Real analysis ; Variable quantities ; ω Infinitesimals Subject RIV AA - Philosophy ; Religion OECD category Philosophy, History and Philosophy of science and technology R&D Projects GJ19-03125Y GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support FLU-F - RVO:67985955 UT WOS 000517656500003 EID SCOPUS 85072232956 DOI 10.1016/j.hm.2019.07.002 Annotation Amid the debate over infinitesimals, Bolzano introduced the alternative notion of variable quantities ω in his 1816 work on the binomial theorem. It has often been assumed that his 1817 definition of continuity using them is practically the modern one. This paper explores Bolzano’s early mathematical works and diaries to gain insight into the subtleties in his definition of ω and some of his mathematical procedures. We show that those quantities are not clearly ‘proto-Weierstrassian’ and argue that Bolzano was in the process of refinement and increasing abstraction of the idea of quantity that eventually led to the development of a theory of real numbers. Workplace Institute of Philosophy Contact Chlumská Simona, chlumska@flu.cas.cz ; Tichá Zuzana, asep@flu.cas.cz Tel: 221 183 360 Year of Publishing 2021 Electronic address https://doi.org/10.1016/j.hm.2019.07.002
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