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# infinitesimal

[in-fin-i-tes-uh-muh l] /ˌɪn fɪn ɪˈtɛs ə məl/
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
1645-1655
1645-55; < Neo-Latin infīnītēsim(us), equivalent to Latin infīnīt(us) infinite + -ēsimus suffix of ordinal numerals + -al1
Related forms
infinitesimality, infinitesimalness, noun
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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Examples from the web for infinitesimals
• Historically, the first method of doing so was by infinitesimals.
• They capture smallscale behavior, just like infinitesimals, but use ordinary numbers.
• Uses synthetic differential geometry and nilpotent infinitesimals.
British Dictionary definitions for infinitesimals

## 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
noun
3.
(maths) an infinitesimal quantity
Derived Forms
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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Word Origin and History for infinitesimals

## infinitesimal

1710 (1650s as a noun), "infinitely small," from Modern Latin infinitesimus, from Latin infinitus "infinite" (see infinite) + -esimus, as in centesimus "hundredth." Related: Infinitesimally.

Online Etymology Dictionary, © 2010 Douglas Harper
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infinitesimals in Science
 infinitesimal   (ĭn'fĭn-ĭ-těs'ə-məl)    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
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Encyclopedia Article for infinitesimals

## 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.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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### Difficulty index for infinitesimal

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### Word Value for infinitesimals

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