indefinitely or exceedingly small; minute: infinitesimal vessels in the circulatory system.
immeasurably small; less than an assignable quantity: to an infinitesimal degree.
of, pertaining to, or involving infinitesimals.
an infinitesimal quantity.
Mathematics. a variable having zero as a limit.

1645–55; < Neo-Latin infīnītēsim(us), equivalent to Latin infīnīt(us) infinite + -ēsimus suffix of ordinal numerals + -al1

infinitesimality, infinitesimalness, noun
infinitesimally, adverb Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
infinitesimal (ˌɪnfɪnɪˈtɛsɪməl)
1.  infinitely or immeasurably small
2.  maths of, relating to, or involving a small change in the value of a variable that approaches zero as a limit
3.  maths an infinitesimal quantity

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Word Origin & History

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, © 2010 Douglas Harper
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American Heritage
Science Dictionary
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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Encyclopedia Britannica


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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Example sentences
Neither infinitesimal time nor infinitesimal space is possible.
But this temporal frame captures only a tiny portion-in fact, an infinitesimal
  one-of the entire future.
We do not and never will due to the infinity and infinitesimal nature of the
It encourages people to invest their dreams, their hopes for a better future,
  into an infinitesimal probability.
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