Matches in SemOpenAlex for { <https://semopenalex.org/work/W2610974781> ?p ?o ?g. }
Showing items 1 to 63 of
63
with 100 items per page.
- W2610974781 abstract "This paper examines the Eulerian notion of infinitesimal or evanescent quantity and compares it with the modern notion of limit and non-standard analysis concepts. The Eulerian infinitesimal, when interpreted using the conceptual instruments available to modern mathematics, seems to be a fluid mixture of different elements, a continuous leap from a vague idea of limit to a confused notion of infinitesimal. However, while the modern notions of limit, hyperreal numbers etc. derive from precise definitions or constructions and are developed within non-equivocal contexts, Euler did not define the notion of evanescent quantity, either explicitly or implicitly: it is substantially a 'common notion', directly derived from the experience of physical and geometric quantities, which can diminish until they vanish. Infinitesimals are fictions, useful instruments for dealing with finite quantities, and thus Euler could state that the algorithm of the calculus did not concern differentials but functions. The vague and imprecise Eulerian notions can be reformulated in modern terms only by introducing extraneous elements into Euler's work and changing the logical and conceptual frame-work of his mathematics." @default.
- W2610974781 created "2017-05-12" @default.
- W2610974781 creator A5089367666 @default.
- W2610974781 date "2012-01-03" @default.
- W2610974781 modified "2023-09-25" @default.
- W2610974781 title "Euler, infinitesimals and limits" @default.
- W2610974781 hasPublicationYear "2012" @default.
- W2610974781 type Work @default.
- W2610974781 sameAs 2610974781 @default.
- W2610974781 citedByCount "0" @default.
- W2610974781 crossrefType "journal-article" @default.
- W2610974781 hasAuthorship W2610974781A5089367666 @default.
- W2610974781 hasConcept C111472728 @default.
- W2610974781 hasConcept C134306372 @default.
- W2610974781 hasConcept C138885662 @default.
- W2610974781 hasConcept C151201525 @default.
- W2610974781 hasConcept C199343813 @default.
- W2610974781 hasConcept C2777686260 @default.
- W2610974781 hasConcept C33923547 @default.
- W2610974781 hasConcept C43058520 @default.
- W2610974781 hasConcept C53469067 @default.
- W2610974781 hasConcept C62884695 @default.
- W2610974781 hasConcept C71924100 @default.
- W2610974781 hasConcept C91229774 @default.
- W2610974781 hasConceptScore W2610974781C111472728 @default.
- W2610974781 hasConceptScore W2610974781C134306372 @default.
- W2610974781 hasConceptScore W2610974781C138885662 @default.
- W2610974781 hasConceptScore W2610974781C151201525 @default.
- W2610974781 hasConceptScore W2610974781C199343813 @default.
- W2610974781 hasConceptScore W2610974781C2777686260 @default.
- W2610974781 hasConceptScore W2610974781C33923547 @default.
- W2610974781 hasConceptScore W2610974781C43058520 @default.
- W2610974781 hasConceptScore W2610974781C53469067 @default.
- W2610974781 hasConceptScore W2610974781C62884695 @default.
- W2610974781 hasConceptScore W2610974781C71924100 @default.
- W2610974781 hasConceptScore W2610974781C91229774 @default.
- W2610974781 hasLocation W26109747811 @default.
- W2610974781 hasOpenAccess W2610974781 @default.
- W2610974781 hasPrimaryLocation W26109747811 @default.
- W2610974781 hasRelatedWork W1005866000 @default.
- W2610974781 hasRelatedWork W114415018 @default.
- W2610974781 hasRelatedWork W1559418938 @default.
- W2610974781 hasRelatedWork W1571027934 @default.
- W2610974781 hasRelatedWork W1580496021 @default.
- W2610974781 hasRelatedWork W1594587727 @default.
- W2610974781 hasRelatedWork W2060680556 @default.
- W2610974781 hasRelatedWork W2081076776 @default.
- W2610974781 hasRelatedWork W2106110500 @default.
- W2610974781 hasRelatedWork W2898407575 @default.
- W2610974781 hasRelatedWork W2963042348 @default.
- W2610974781 hasRelatedWork W2967108677 @default.
- W2610974781 hasRelatedWork W3006094945 @default.
- W2610974781 hasRelatedWork W3010623865 @default.
- W2610974781 hasRelatedWork W3042129887 @default.
- W2610974781 hasRelatedWork W3214587444 @default.
- W2610974781 hasRelatedWork W56752780 @default.
- W2610974781 hasRelatedWork W577449674 @default.
- W2610974781 hasRelatedWork W63047686 @default.
- W2610974781 hasRelatedWork W1969966114 @default.
- W2610974781 isParatext "false" @default.
- W2610974781 isRetracted "false" @default.
- W2610974781 magId "2610974781" @default.
- W2610974781 workType "article" @default.