in·​fin·​i·​tes·​i·​mal | \ (ˌ)in-ˌfi-nə-ˈte-sə-məl How to pronounce infinitesimal (audio) , -zə-məl \

Definition of infinitesimal

 (Entry 1 of 2)

1 : immeasurably or incalculably small an infinitesimal difference
2 : taking on values arbitrarily close to but greater than zero



Definition of infinitesimal (Entry 2 of 2)

: an infinitesimal quantity or variable

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Other Words from infinitesimal


infinitesimally \ (ˌ)in-​ˌfi-​nə-​ˈte-​sə-​mə-​lē How to pronounce infinitesimal (audio) , -​zə-​mə-​ \ adverb

What is the origin of infinitesimal?


Infinite, as you probably know, means "endless" or "extending indefinitely." It is ultimately from Latin infinitus, the opposite of finitus, meaning "finite." The notion of smallness in infinitesimal derives from the mathematical concept that a quantity can be divided endlessly; no matter how small, it can be subdivided into yet smaller fractions, or "infinitesimals." The concept was still in its infancy in 1710 when Irish philosopher George Berkeley observed that some people "assert there are infinitesimals of infinitesimals of infinitesimals, etc., without ever coming to an end." He used the adjective in a mathematical sense, too, referring to "infinitesimal parts of finite lines." Less than a quarter century later, the adjective had acquired a general sense applicable to anything too small to be measured.

Examples of infinitesimal in a Sentence

Adjective an infinitesimal moment in time a soft drink with only an infinitesimal amount of caffeine
Recent Examples on the Web: Adjective The Alabama Republican said the issue was far from the most important in the military and proceeded to cite infinitesimal statistics for separation related to extremism. Abraham Mahshie, Washington Examiner, "Defense Department denies being ‘thought police’ in launch of extremism study," 9 Apr. 2021 But if there were, Oakland Mills’ chances late in the game to come back and beat Mt. Hebron, 18-14, on Friday would’ve been infinitesimal. Brent Kennedy,, "Late touchdown seals Oakland Mills comeback win over Mt. Hebron | Howard County football roundup," 19 Mar. 2021 The syringes also must have low dead space — the infinitesimal distance between the plunger and the needle after the dose is fully injected — to minimize waste. New York Times, "The World Needs Syringes. He Jumped In to Make 5,900 Per Minute.," 5 Mar. 2021 Quantum mechanics, the theory governing the infinitesimal world, doesn't allow for nothingness. Clara Moskowitz, Scientific American, "The Cosmological Constant Is Physics’ Most Embarrassing Problem," 1 Feb. 2021 Newtonian physics, once thought to govern the entire natural world, turned out to collapse at the infinitesimal scale, where the probabilistic features of quantum mechanics take over. Michael Hiltzik, Los Angeles Times, "Column: Why I never ‘agree to disagree’ — I just tell you you’re wrong," 22 Dec. 2020 Fishing rights, which amounts to an infinitesimal sliver of trade between the neighbors, is the last big holdup. Bernhard Warner, Fortune, "How high can Bitcoin go? The bulls say this rally has only just begun," 17 Dec. 2020 Even an infinitesimal risk of error is too great to justify the Doomsday Machine’s existence. Adrienne Lafrance, The Atlantic, "Facebook Is a Doomsday Machine," 15 Dec. 2020 The Detroit Lions' slim playoff hopes fell to almost infinitesimal levels with Sunday's loss to the Green Bay Packers, but that has not dampened interim head coach Darrell Bevell's outlook on the final three games. Dave Birkett, Detroit Free Press, "Detroit Lions' playoff hopes slip to 2%: 'So you're saying there's a chance'," 14 Dec. 2020 Recent Examples on the Web: Noun This led to his theory of surreal numbers — a huge new number system containing not only all the real numbers, but also a boggling collection of infinites and infinitesimals, like π minus 1 divided by the cube root of infinity. New York Times, "Travels with John Conway, in 258 Septillion Dimensions," 16 May 2020 Infinities implicitly pervade many familiar mathematical concepts, such as the idea of points as mentioned above, the idea of the continuum, and the concept of infinitesimals in calculus. Quanta Magazine, "Is Infinity Real?," 16 June 2016

These example sentences are selected automatically from various online news sources to reflect current usage of the word 'infinitesimal.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

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First Known Use of infinitesimal


1710, in the meaning defined at sense 2


1706, in the meaning defined above

History and Etymology for infinitesimal


borrowed from New Latin infīnītēsimālis, from infīnītēsimus "infinite in rank" (from Latin infīnītus "having no limit, infinite entry 1" + -ēsimus, suffix of higher ordinal numbers) + Latin -ālis -al entry 1 — more at vigesimal


New Latin infīnītēsimus "infinite in rank" + -al entry 2 — more at infinitesimal entry 1

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Time Traveler for infinitesimal

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The first known use of infinitesimal was in 1706

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Last Updated

17 Apr 2021

Cite this Entry

“Infinitesimal.” Dictionary, Merriam-Webster, Accessed 19 Apr. 2021.

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More Definitions for infinitesimal



English Language Learners Definition of infinitesimal

: extremely small


in·​fin·​i·​tes·​i·​mal | \ in-ˌfi-nə-ˈte-sə-məl How to pronounce infinitesimal (audio) \

Kids Definition of infinitesimal

: extremely small The chance of winning is infinitesimal.

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