The notion of variable quantities ω in Bolzano’s early works

0535527 - FLÚ 2021 RIV US eng J - Journal Article
Fuentes Guillén, Elías - Martínez Adame, C.
The notion of variable quantities ω in Bolzano’s early works.
Historia Mathematica. -, č. 50 (2020), s. 25-49. ISSN 0315-0860. E-ISSN 1090-249X
R&D Projects: GA ČR(CZ) GJ19-03125Y
Institutional support: RVO:67985955
Keywords : History of nineteenth century * mathematics * Bolzano * Real analysis * Variable quantities * ω Infinitesimals
OECD category: Philosophy, History and Philosophy of science and technology
Impact factor: 0.639, year: 2020
Method of publishing: Limited access
https://doi.org/10.1016/j.hm.2019.07.002

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.
Permanent Link: http://hdl.handle.net/11104/0313525