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infinitesimal - 7 dictionary results

in⋅fin⋅i⋅tes⋅i⋅mal

  [in-fin-i-tes-uh-muhl]
Use infinitesimal in a Sentence
–adjective
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.
–noun
4. an infinitesimal quantity.
5. Mathematics. a variable having zero as a limit.
Origin:
1645–55; < NL infīnītēsim(us), equiv. to L infīnīt(us) infinite + -ēsimus suffix of ordinal numerals + -al 1

Related forms:
in⋅fin⋅i⋅tes⋅i⋅mal⋅i⋅ty, in⋅fin⋅i⋅tes⋅i⋅mal⋅ness, noun
in⋅fin⋅i⋅tes⋅i⋅mal⋅ly, adverb
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2009.
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in·fin·i·tes·i·mal   (ĭn'fĭn-ĭ-těs'ə-məl)   
adj.  
  1. Immeasurably or incalculably minute.
  2. Mathematics Capable of having values approaching zero as a limit.
n.  
  1. An immeasurably or incalculably minute amount or quantity.
  2. Mathematics A function or variable continuously approaching zero as a limit.

[From New Latin īnfīnītēsimus, infinite in rank, from Latin īnfīnītus, infinite; see infinite.]
in'fin·i·tes'i·mal·ly adv.
The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2009 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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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.

Infinitesimal calculus, the different and the integral calculus, when developed according to the method used by Leibnitz, who regarded the increments given to variables as infinitesimal.

Infinitesimal

In`fin*i*tes"i*mal\, n. (Math.) An infinitely small quantity; that which is less than any assignable quantity.
Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
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infinitesimal  (adj.)
1710, "infinitely small," from Mod.L. infinitesimus, coined by Ger. philosopher and mathematician Baron Gottfried Wilhelm von Leibniz (1646-1716) from L. infinitus "infinite" (see infinite) + -esimus, as in centesimus "hundredth."
Online Etymology Dictionary, © 2001 Douglas Harper
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infinitesimal   (ĭn'fĭn-ĭ-těs'ə-məl)  Pronunciation Key 
Adjective   Capable of having values approaching zero as a limit.

Noun   A function or variable continuously approaching zero as a limit.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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infinitesimal

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 were defined as ultimate ratios of infinitesimals, and integrals 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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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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