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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

60301 - Philosophy, History and Philosophy of science and technology

Projekt

<a href="/cs/project/GJ19-03125Y" target="_blank" >GJ19-03125Y: Matematika v Českých zemích: od jezuitského učení po Bernarda Bolzana</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

HISTORIA MATHEMATICA

ISSN

1090-249X

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

50

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

25

Strana od-do

25-49

Kód UT WoS článku

000517656500003

EID výsledku v databázi Scopus

2-s2.0-85072232956