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In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus , which originally referred to the " infinity - eth " item in a sequence .
Jean Alexandre Eugène Dieudonné (French: [ʒɑ̃ alɛksɑ̃dʁ øʒɛn djødɔne]; 1 July 1906 – 29 November 1992) was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a ...
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Abraham Robinson (born Robinsohn; [1] October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics.
In his 1821 book Cours d'analyse, Augustin-Louis Cauchy discussed variable quantities, infinitesimals and limits, and defined continuity of = by saying that an infinitesimal change in x necessarily produces an infinitesimal change in y, while Grabiner claims that he used a rigorous epsilon-delta definition in proofs. [2]
A hyperreal r is infinitesimal if and only if it is infinitely close to 0. For example, if n is a hyperinteger, i.e. an element of *N − N, then 1/n is an infinitesimal. A hyperreal r is limited (or finite) if and only if its absolute value is dominated by (less than) a standard integer.
In mathematics, the term infinitesimal generator may refer to: an element of the Lie algebra, associated to a Lie group; Infinitesimal generator (stochastic processes), of a stochastic process; infinitesimal generator matrix, of a continuous time Markov chain, a class of stochastic processes; Infinitesimal generator of a strongly continuous ...
Johann Bernoulli [a] (also known as Jean in French or John in English; 6 August [O.S. 27 July] 1667 – 1 January 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family.