# infinitesimal

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in·​fin·​i·​tes·​i·​mal (ˌ)in-ˌfi-nə-ˈte-sə-məl
-zə-məl
1
: immeasurably or incalculably small
an infinitesimal difference
2
: taking on values arbitrarily close to but greater than zero

infinitesimal

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## noun

: an infinitesimal quantity or variable

## Did you know?

What is the origin of infinitesimal?

Infinite, as you probably know, means "endless" or "extending indefinitely." It is ultimately from Latin infīnītus, the opposite of fīnītus, 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 the early 1700s 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 word in a mathematical sense, too, referring to "infinitesimal parts of finite lines." Later, the adjectival form 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
That comprises an infinitesimal number of the more than 500,000 participants in NCAA athletics. Rudy Chinchilla, NBC News, 7 Apr. 2024 Their star is stachybotrys chartarum, a black mold reported to produce infinitesimal quantities of a toxin similar to botulism. Kelly G. Richardson, Orange County Register, 22 Mar. 2024 Haley’s 20-point defeat means the former governor and UN ambassador has an infinitesimal chance of thwarting Trump's path to the Republican presidential nomination. Emma Hinchliffe, Fortune, 26 Feb. 2024 The chances anyone would lose all three of those games are infinitesimal. Josh Dubow, USA TODAY, 14 Feb. 2024 Most stars are so far away from Earth that their apparent brightness is only an infinitesimal fraction of their actual glory. Phil Plait, Scientific American, 4 Aug. 2023 Musser shows that prodding at the level of infinitesimal quantum phenomena uncovers larger questions that require a fuller understanding of our consciousness. Pitchaya Sudbanthad, Scientific American, 1 Dec. 2023 Given that Democratic chances to hold on to their slim majority in the House are already small, if not infinitesimal, polling errors could mean that Republicans are still on their way to retaking both chambers of Congress in the new year—the result that history teaches us to expect. Alex Shephard, The New Republic, 14 Sep. 2022 With the rise of frequency, as well as quantum mechanics, time began to be constructed from the ground up, using the infinitesimal frequencies of atoms, rather than from above, using the movement of celestial objects. Tom Vanderbilt, Harper’s Magazine , 13 Mar. 2023
Noun
Initially, Newton and Leibniz came up with objects called infinitesimals. Jordana Cepelewicz, Quanta Magazine, 31 Aug. 2023 The one that resounds with the strongest symbolic power is a cinematic infinitesimal: Gia’s prepaid cell phone, which speaks to her in a robo-voice of her declining balance, dwindling ominously to ninety-six cents when Trey calls her, four when her water breaks. Richard Brody, The New Yorker, 13 July 2023 Since then, Parker has persistently sought meaning in the infinitesimal and evanescent. Jonathon Keats, Forbes, 20 May 2022 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, 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, 16 June 2016

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'infinitesimal.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

## Word History

Etymology

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

Noun

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

First Known Use

1710, in the meaning defined at sense 2

Noun

1706, in the meaning defined above

Time Traveler
The first known use of infinitesimal was in 1706

infinitesimal

## Cite this Entry

“Infinitesimal.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/infinitesimal. Accessed 23 Apr. 2024.

## Kids Definition

infinitesimal

in·​fin·​i·​tes·​i·​mal
(ˌ)in-ˌfin-ə-ˈtes-ə-məl
: too small to be measurable
infinitesimally
-mə-lē