The notion of variable quantities ω in Bolzano’s early works
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985955%3A_____%2F20%3A00535527" target="_blank" >RIV/67985955:_____/20:00535527 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.hm.2019.07.002" target="_blank" >https://doi.org/10.1016/j.hm.2019.07.002</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.hm.2019.07.002" target="_blank" >10.1016/j.hm.2019.07.002</a>
Alternative languages
Result language
angličtina
Original language name
The notion of variable quantities ω in Bolzano’s early works
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
60301 - Philosophy, History and Philosophy of science and technology
Result continuities
Project
<a href="/en/project/GJ19-03125Y" target="_blank" >GJ19-03125Y: Mathematics in the Czech lands: from the Jesuit teaching to Bernard Bolzano</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
HISTORIA MATHEMATICA
ISSN
1090-249X
e-ISSN
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Volume of the periodical
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Issue of the periodical within the volume
50
Country of publishing house
US - UNITED STATES
Number of pages
25
Pages from-to
25-49
UT code for WoS article
000517656500003
EID of the result in the Scopus database
2-s2.0-85072232956