infinitesimal

See also: infinitésimal

English

Etymology

From Latin infinitesimus, from infinitus (“infinite”) + -esimus, as in centesimus (“hundredth”).

Pronunciation

• IPA^(key): /ˌɪnfɪnɪˈtɛsɪməl/

• Audio (US):

  (file)

Adjective

infinitesimal (comparative more infinitesimal, superlative most infinitesimal)

1. Incalculably, exceedingly, or immeasurably minute; vanishingly small.

   Do you ever get the feeling that you are but an infinitesimal speck, swallowed by the vastness of the universe and beyond?

   • 1913, Sir Arthur Conan Doyle, The Poison Belt‎^[1]:

     "You will conceive a bunch of grapes," said he, "which are covered by some infinitesimal but noxious bacillus."

   • 2001, Eoin Colfer, Artemis Fowl, page 221:

     Then you could say that the doorway exploded. But the particular verb doesn't do the action justice. Rather, it shattered into infinitesimal pieces.

2. (mathematics) Of or pertaining to values that approach zero as a limit.
3. (informal) Very small.

Usage notes

• Strictly, this adjective, like infinite, is incomparable, so more infinitesimal and most infinitesimal are proscribed, especially in the mathematical sense. However, these forms do occur in informal usage, where the very small (but measurable) sense is most common.

• The mathematical usage is very difficult to grasp for a non-expert, because the infinitesimal value is a fiction that represents an abstract concept with a convenient idiom. In calculus, a calculation can get ever closer to a known result, the limit, as one of its component values gets ever closer to zero; but there is no actual value small enough to produce that result. The infinitesimal value is the fictional smallest of all numbers, which results, impossibly, in the limit being calculated. Mathematicians know there is no such thing as the smallest non-zero number, but this idiomatic fiction spares them from impossibly complex descriptions. For the lay person, a convenient definition of the mathematical usage is impossibly small. Much colloquial usage undoubtedly emerges from the humorous hyperbole of declaring something impossibly small, by people aware of the mathematical meaning.

Synonyms

• See also Thesaurus:tiny

Antonyms

• infinite
• enormous

Translations

very small

• Bulgarian: безкрайно малък (bezkrajno malǎk)
• Czech: nepatrný (cs)
• Dutch: (jargon) infinitesimaal (nl), (colloquial) oneindig klein
• Finnish: äärettömän pieni, infinitesimaalinen
• French: infinitésimal
• Greek: απειροελάχιστος (el) m (apeiroeláchistos)
• (deprecated template usage) {{trans-mid}}
• Hebrew: אַפְסִי m (afsí)
• Maori: merowhetau
• Polish: nieskończenie mały m
• Russian: бесконе́чно ма́лый (beskonéčno mályj)
• Serbo-Croatian: инфинитезималан
• Tagalog: napakalinggit

mathematics: pertaining to values that approach zero

• Bulgarian: клонящ към нула (klonjašt kǎm nula)
• Czech: infinitezimální
• Finnish: infinitesimaalinen
• (deprecated template usage) {{trans-mid}}
• Greek: απειροστός (el) m (apeirostós)
• Polish: nieskończenie mały m
• Tagalog: napakalinggit

Noun

infinitesimal (plural infinitesimals)

1. (mathematics) A non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number).

Antonyms

• infinity

Derived terms

• infinitesimal calculus
• infinitesimally

Translations

A non-zero quantity whose magnitude is smaller than any positive number

• Finnish: infinitesimaali
• French: infinitésimal (fr)
• Greek: πολλοστημόριο (el) n (pollostimório)
• Hungarian: infinitezimális
• (deprecated template usage) {{trans-mid}}
• Russian: бесконе́чно малая величина́ f (beskonéčno malaja veličiná)
• Swedish: infinitesimal (sv)
• Tagalog: napakalinggit

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Spanish

Pronunciation

• IPA^(key): /infinitesiˈmal/ [ĩɱ.fi.ni.t̪e.siˈmal]

Adjective

infinitesimal m or f (masculine and feminine plural infinitesimales)

1. infinitesimal

Derived terms

• cálculo infinitesimal m (“infinitesimal calculus”)
• infinitesimalmente

Further reading

• “infinitesimal”, in Diccionario de la lengua española, Vigésima tercera edición, Real Academia Española, 2014