# infinitesimal

infinitesimal
1. indefinitely or exceedingly small; minute: infinitesimal vessels in the circulatory system.
2. immeasurably small; less than an assignable quantity: to an infinitesimal degree.
3. of, pertaining to, or involving infinitesimals.
n.
4. an infinitesimal quantity.
5. Math. a variable having zero as a limit.
[1645-55; < NL infinitesim(us), equiv. to L infinit(us) INFINITE + -esimus suffix of ordinal numerals + -AL1]

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in mathematics, a quantity less than any finite quantity yet not zero. Even though no such quantity can exist in the real number system, many early attempts to justify calculus were based on sometimes dubious reasoning about infinitesimals: derivatives (derivative) were defined as ultimate ratios of infinitesimals, and integrals (integral) were calculated by summing rectangles of infinitesimal width. As a result, differential and integral calculus was originally referred to as the infinitesimal calculus. This terminology gradually disappeared as rigorous concepts of limit, continuity, and the real numbers were formulated.

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Universalium. 2010.

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• 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