Generality of algebra

In the <a href="/facts/History_of_mathematics/18h5rQA5">history of mathematics</a>, the generality of algebra was a phrase used by <a href="/facts/Augustin-Louis_Cauchy/aoTjgj6j">Augustin-Louis Cauchy</a> to describe a method of argument that was used in the 18th century by mathematicians such as <a href="/facts/Leonhard_Euler/z2fsbjgj">Leonhard Euler</a> and <a href="/facts/Joseph-Louis_Lagrange/bTQUaSTv">Joseph-Louis Lagrange</a>, particularly in manipulating <a href="/facts/Infinite_series/yDnlsgIe">infinite series</a>. According to Koetsier, the generality of algebra principle assumed, roughly, that the <a href="/facts/Algebra/nMdqczjo">algebraic</a> rules that hold 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 <a href="/facts/Calculus/MEmUTYoz">calculus</a> that hold for finite expansions even when manipulating infinite expansions. 
In works such as <a href="/facts/Cours_d%2527Analyse/IUUvmV23">Cours d'Analyse</a>, Cauchy rejected the use of "generality of algebra" methods and sought a more <a href="/facts/Rigour/v23FKfhw">rigorous</a> foundation for <a href="/facts/Mathematical_analysis/XXeR26Ih">mathematical analysis</a>.

Generality of algebra open-in-new

Generality of algebra