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- Generality_of_algebra abstract "In the history of mathematics, the generality of algebra was a phrase used by Augustin-Louis Cauchy to describe a method of argument that was used in the 18th century by mathematicians such as Leonhard Euler and Joseph-Louis Lagrange, particularly in manipulating infinite series. According to Koetsier, the generality of algebra principle assumed, roughly, that the algebraic rules that hold obviously for a certain class of expressions can be extended to hold more generally on a larger class of objects, even if the rules are no longer obviously valid. As a consequence, 18th century mathematicians believed that they could derive meaningful results by applying the usual rules of algebra and calculus that hold for finite expansions even when manipulating infinite expansions. In works such as Cours d'Analyse, Cauchy rejected the use of "generality of algebra" methods and sought a more rigorous foundation for mathematical analysis.An example is Euler's derivation of the series</dl>for . He first evaluated the identityat to obtainThe infinite series on the right hand side of this expression diverges for all real . But nevertheless integrating this term-by-term gives (1), an identity which is known to be true by modern methods.".
- Generality_of_algebra wikiPageID "31628660".
- Generality_of_algebra wikiPageRevisionID "577687978".
- Generality_of_algebra hasPhotoCollection Generality_of_algebra.
- Generality_of_algebra subject Category:History_of_calculus.
- Generality_of_algebra subject Category:Mathematical_analysis.
- Generality_of_algebra comment "In the history of mathematics, the generality of algebra was a phrase used by Augustin-Louis Cauchy to describe a method of argument that was used in the 18th century by mathematicians such as Leonhard Euler and Joseph-Louis Lagrange, particularly in manipulating infinite series.".
- Generality_of_algebra label "Generality of algebra".
- Generality_of_algebra sameAs m.0gmd1k4.
- Generality_of_algebra sameAs Q5532420.
- Generality_of_algebra sameAs Q5532420.
- Generality_of_algebra wasDerivedFrom Generality_of_algebra?oldid=577687978.
- Generality_of_algebra isPrimaryTopicOf Generality_of_algebra.