Both the infinitely large and its inverse, the infinitely small, cause headaches. The first philosophical explorations that turned disquiet into something more tangible were Zeno's paradoxes . The 18th-century development of the calculus led to the consideration of magnitudes changing over ‘indefinitely’ smaller intervals of time, and the reaction on Zeno's behalf came from Berkeley, who saw that the infinitesimals resulting (‘the vanished ghosts of departed quantities’) were treated inconsistently as finite quantities or as nothing, depending on the exigencies of the argument. A rigorous treatment of the notion of a limit was only provided by K. T. W. Weierstrass (1815–97) in the 19th century: it need only refer to finite numbers, and thus removes the place of the infinitesimal from the foundations of mathematics. However, a consistent non-standard analysis has been developed by the mathematician Abraham Robinson (1918–74): in it infinitesimals have the disturbing property that while they are not nothing, no sum of n of them is ever greater than any finite number, so the number sequence that includes them is not Archimedean.

Philosophy dictionary. . 2011.


Look at other dictionaries:

  • infinitésimal — infinitésimal, ale, aux [ ɛ̃finitezimal, o ] adj. • 1706; de l adj. infinitésime, lat. mod. infinitesimus 1 ♦ Sc. Relatif aux quantités infiniment petites. Calcul infinitésimal, analyse infinitésimale : partie des mathématiques comprenant le… …   Encyclopédie Universelle

  • Infinitesimal — In fin*i*tes i*mal, a. [Cf. F. infinit[ e]simal, fr. infinit[ e]sime infinitely small, fr. L. infinitus. See {Infinite}, a.] Infinitely or indefinitely small; less than any assignable quantity or value; very small. [1913 Webster] {Infinitesimal… …   The Collaborative International Dictionary of English

  • infinitesimal — (Del fr. infinitésimal). adj. Mat. Perteneciente o relativo a las cantidades infinitamente pequeñas. U. t. c. s. m.) ☛ V. cálculo infinitesimal …   Diccionario de la lengua española

  • infinitesimal — [in΄fin i tes′i məl, in΄fin itez′i məl] adj. [ModL infinitesimus < L infinitus (see INFINITE), infl. by centesimus, hundredth < centum, HUNDRED] 1. too small to be measured; infinitely small 2. Math. of or pertaining to an infinitesimal n.… …   English World dictionary

  • infinitésimal — infinitésimal, ale (in fi ni té zi mal, ma l ) adj. Terme de mathématique. Qui a le caractère d une quantité infiniment petite. •   Le plus vil métal recouvert d une couche infinitésimale d or ou d argent par les procédés de la galvanoplastie,… …   Dictionnaire de la Langue Française d'Émile Littré

  • infinitesimal — adj. 2 g. 1.  [Matemática] Que tem o caráter de infinitésima. 2. Composto de partes infinitamente pequenas. 3. cálculo infinitesimal: cálculo que compreende o integral e o diferencial …   Dicionário da Língua Portuguesa

  • infinitesimal — adjetivo 1. Área: matemáticas [Cantidad] que es infinitamente pequeña. cálculo* infinitesimal …   Diccionario Salamanca de la Lengua Española

  • Infinitesimal — In fin*i*tes i*mal, n. (Math.) An infinitely small quantity; that which is less than any assignable quantity. [1913 Webster] …   The Collaborative International Dictionary of English

  • infinitesimal — index impalpable, inappreciable, intangible, minimal, tenuous Burton s Legal Thesaurus. William C. Burton. 2006 …   Law dictionary

  • infinitésimal — INFINITÉSIMAL: On ne sait pas ce que c est, mais a rapport à l homéopathie …   Dictionnaire des idées reçues

  • infinitesimal — (adj.) 1710 (1650s as a noun), infinitely small, from Mod.L. infinitesimus, from L. infinitus infinite (see INFINITE (Cf. infinite)) + esimus, as in centesimus hundredth. Related: Infinitesimally …   Etymology dictionary

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