### What does **infinitesimal** mean?

# Definitions for infinitesimal

ˌɪn fɪn ɪˈtɛs ə məlin·fin·i·tes·i·mal

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **infinitesimal**.

### Princeton's WordNet

infinitesimaladjective

(mathematics) a variable that has zero as its limit

infinitesimal, minuteadjective

infinitely or immeasurably small

"two minute whiplike threads of protoplasm"; "reduced to a microscopic scale"

### Wiktionary

infinitesimalnoun

A non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number).

infinitesimaladjective

Incalculably, exceedingly, or immeasurably minute; vanishingly small.

Do you ever get the feeling that you are but an infinitesimal speck, swallowed by the vastness of the universe and beyond?

infinitesimaladjective

Of or pertaining to values that approach zero as a limit.

infinitesimaladjective

Very small.

### Samuel Johnson's Dictionary

Infinitesimaladjective

Infinitely divided.

**Etymology:**from*infinite.*

### Wikipedia

Infinitesimal

In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinity-th" item in a sequence. Infinitesimals do not exist in the standard real number system, but they do exist in other number systems, such as the surreal number system and the hyperreal number system, which can be thought of as the real numbers augmented with both infinitesimal and infinite quantities; the augmentations are the reciprocals of one another. Infinitesimal numbers were introduced in the development of calculus, in which the derivative was first conceived as a ratio of two infinitesimal quantities. This definition was not rigorously formalized. As calculus developed further, infinitesimals were replaced by limits, which can be calculated using the standard real numbers. Infinitesimals regained popularity in the 20th century with Abraham Robinson's development of nonstandard analysis and the hyperreal numbers, which, after centuries of controversy, showed that a formal treatment of infinitesimal calculus was possible. Following this, mathematicians developed surreal numbers, a related formalization of infinite and infinitesimal numbers that include both hyperreal cardinal and ordinal numbers, which is the largest ordered field.

### ChatGPT

infinitesimal

Infinitesimal refers to a quantity or object that is indefinitely small or extremely close to zero, but not exactly zero. In calculus and mathematics, it's often used to express the idea of quantities that are so small they are practically negligible, yet they still have an impact on calculations. It's a fundamental concept in differential calculus where it's used to describe rates of change and the slope of curves. The concept of infinitesimal has also been applied in various other scientific fields such as physics and engineering.

### Webster Dictionary

Infinitesimaladjective

infinitely or indefinitely small; less than any assignable quantity or value; very small

Infinitesimalnoun

an infinitely small quantity; that which is less than any assignable quantity

**Etymology:**[Cf. F. infinitsimal, fr. infinitsime infinitely small, fr. L. infinitus. See Infinite, a.]

### Wikidata

Infinitesimal

Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. The insight with exploiting infinitesimals was that objects could still retain certain specific properties, such as angle or slope, even though these objects were quantitatively small. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a series. It was originally introduced around 1670 by either Nicolaus Mercator or Gottfried Wilhelm Leibniz. In common speech, an infinitesimal object is an object which is smaller than any feasible measurement, but not zero in size; or, so small that it cannot be distinguished from zero by any available means. Hence, when used as an adjective, "infinitesimal" in the vernacular means "extremely small". In order to give it a meaning it usually has to be compared to another infinitesimal object in the same context. Infinitely many infinitesimals are summed to produce an integral. Archimedes used what eventually came to be known as the Method of indivisibles in his work The Method of Mechanical Theorems to find areas of regions and volumes of solids. In his formal published treatises, Archimedes solved the same problem using the Method of Exhaustion. The 15th century saw the work of Nicholas of Cusa, further developed in the 17th century by Johannes Kepler, in particular calculation of area of a circle by representing the latter as an infinite-sided polygon. Simon Stevin's work on decimal representation of all numbers in the 16th century prepared the ground for the real continuum. Bonaventura Cavalieri's method of indivisibles led to an extension of the results of the classical authors. The method of indivisibles related to geometrical figures as being composed of entities of codimension 1. John Wallis's infinitesimals differed from indivisibles in that he would decompose geometrical figures into infinitely thin building blocks of the same dimension as the figure, preparing the ground for general methods of the integral calculus. He exploited an infinitesimal denoted in area calculations.

### Numerology

Chaldean Numerology

The numerical value of infinitesimal in Chaldean Numerology is:

**6**Pythagorean Numerology

The numerical value of infinitesimal in Pythagorean Numerology is:

**5**

### Examples of infinitesimal in a Sentence

(C)(P) AN

**INFINITESIMAL**AMOUNT OF BLACK, POOR BLACKS,POOR WHITES LIVES HAS BEEN LOST IN AMERICA BEFORE A SIMPLE CAMERA PHONE WAS INVENTED, AND ALLOWED TO BE USED AS EVIDENCE IN A COURT SYSTEM WHICH SPEAKS INJUSTICE AFTER SO MANY YEARS. IT IS MY HOPE THAT THE TECHNOLOGY WE CREATE WILL DO THAT TO SHOW THE TRUTH SO NECESSARY TO DECIDE OUR FATE. THE AHMAUD ARBERY CASE SPEAK THIS TRUTH.Microbiology is a journey through the invisible kingdoms, exploring the profound influence of the

**infinitesimal**in shaping the visible world.In reality, the virus clinically no longer exists in Italy, the swabs that were performed over the last 10 days showed a viral load in quantitative terms that was absolutely

**infinitesimal**compared to the ones carried out a month or two months ago.On policy issues, the divide between Sanders and Clinton is almost

**infinitesimal**, compared to the wide gulf between Clinton and Donald Trump or Ted Cruz, clinton has and must continue to make the case that she is the only viable candidate in the race who has and will address those concerns.The swabs that were performed over the last 10 days showed a viral load in quantitative terms that was absolutely

**infinitesimal**compared to the ones carried out a month or two months ago.

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## Translations for **infinitesimal**

### From our Multilingual Translation Dictionary

- متناهى الصغرArabic
- nepatrnýCzech
- infinitesimalSpanish
- بی نهایت کمPersian
- infinitesimaalinen, [[äärettömän]] [[pieni]], infinitesimaaliFinnish
- infinitésimalFrench
- infinitezimálisHungarian
- זָעִיר מְאֹדHebrew
- бесконечно малая величина, бесконечно малыйRussian
- infinitesimalSwedish
- sonsuz küçükTurkish
- ינפאַנאַטעסימאַלYiddish

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"infinitesimal." *Definitions.net.* STANDS4 LLC, 2024. Web. 19 May 2024. <https://www.definitions.net/definition/infinitesimal>.

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