Infinitesimal: meaning, definitions and examples

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infinitesimal

[ɪnˌfɪnɪˈtɛsɪməl ]

Definitions

^{Context #1 | Adjective}

mathematics

Infinitesimal refers to an extremely small quantity, so small that it cannot be measured or distinguished. In mathematics, infinitesimal is used to describe quantities that are infinitely small, approaching zero but not quite zero.

Synonyms

microscopic, minuscule, tiny.

Which Synonym Should You Choose?

Word	Description / Examples
infinitesimal	Used in scientific and mathematical contexts to describe extremely small quantities or sizes. The difference in measurements is infinitesimal and hardly noticeable
tiny	Commonly used in everyday language to describe something very small, often in an informal or general context. She found a tiny kitten in her backyard
minuscule	Used to describe something that is very small in size but not necessarily microscopic or scientific in nature. He wrote his name in minuscule letters at the bottom of the page
microscopic	Applied when discussing objects or organisms that are so small they can only be seen with a microscope. Bacteria are microscopic organisms that can cause diseases

Examples of usage

Calculating the slope of a curve at a specific point often involves dealing with infinitesimal changes in the x and y coordinates.
The concept of infinitesimal is crucial in calculus, where it allows mathematicians to work with limits and derivatives.

^{Context #2 | Noun}

mathematics

In mathematics, an infinitesimal is an infinitely small quantity. It is used to define the concept of limits, derivatives, and integrals in calculus.

Synonyms

infinitely small value, microscopic quantity.

Which Synonym Should You Choose?

Word	Description / Examples
infinitesimal	Used in mathematical or scientific contexts to describe something extremely small or approaching zero. The probability of this event occurring is infinitesimal. In calculus, we often deal with infinitesimal changes in variables.
microscopic quantity	Used in scientific contexts, particularly in biology, chemistry or physics, to describe quantities or objects that require a microscope to be seen. They discovered a microscopic quantity of bacteria in the sample. Even a microscopic quantity of this substance can trigger an allergic reaction.
infinitely small value	Used in general contexts to describe something very small, especially in mathematics, often to emphasize the extremely small size. The difference between the two measurements is an infinitely small value. He understood that the error margin was almost an infinitely small value.

Word

Description / Examples

infinitesimal

Used in mathematical or scientific contexts to describe something extremely small or approaching zero.

The probability of this event occurring is infinitesimal.
In calculus, we often deal with infinitesimal changes in variables.

microscopic quantity

Used in scientific contexts, particularly in biology, chemistry or physics, to describe quantities or objects that require a microscope to be seen.

They discovered a microscopic quantity of bacteria in the sample.
Even a microscopic quantity of this substance can trigger an allergic reaction.

infinitely small value

Used in general contexts to describe something very small, especially in mathematics, often to emphasize the extremely small size.

The difference between the two measurements is an infinitely small value.
He understood that the error margin was almost an infinitely small value.

Examples of usage

When studying the behavior of functions, mathematicians often consider the behavior of functions at infinitesimally close points.
Infinitesimals are fundamental in the development of calculus and the understanding of continuous change.

^{Context #3 | Noun}

general

In everyday language, infinitesimal can refer to something extremely small or insignificant.

Synonyms

minimal, negligible, trivial.

Which Synonym Should You Choose?

Word	Description / Examples
infinitesimal	Used in a scientific or mathematical context to describe something extremely small, almost approaching zero. The differences in their measurements were infinitesimal. The probability of such an event occurring is infinitesimal.
negligible	Indicates that something is so small or unimportant that it can be disregarded, often used in both technical and everyday contexts. The increase in cost was negligible. Any side effects from the medication are negligible.
minimal	Describes something that is the smallest in amount or degree, often in everyday situations, and does not imply a scientific context. The impact on the environment was minimal. She made only minimal changes to the recipe.
trivial	Used to describe something that is very small or unimportant, often in a context that suggests it is not worth considering. The argument was over a trivial matter. His concerns were seen as trivial by the management.

Examples of usage

The impact of his actions was infinitesimal, barely noticeable in the grand scheme of things.

Interesting Facts

Etymology

The word comes from Latin 'infinitesimus', meaning 'infinitely small'.
It was first used in the 17th century, becoming popular in mathematics and calculus.
The concept was developed by mathematicians like Isaac Newton and Gottfried Wilhelm Leibniz, enhancing the understanding of limits and derivatives.

Mathematics

In calculus, infinitesimals are used to help define derivatives, which describe how functions change.
They play a crucial role in the concept of limits, which are the foundation of calculus.
Infinitesimals allow mathematicians to work with very small quantities, essential for solving complex equations.

Physics

Infinitesimally small values come into play in quantum mechanics, where particles exist in states that can be incredibly tiny.
In physics, understanding the infinitesimal helps explain concepts like motion and force at microscopic levels.
Einstein's theory of general relativity uses concepts that involve infinitesimally small curves in spacetime.

Philosophy

Infinitesimals brought philosophical debates about the nature of space, time, and existence, especially during the early modern period.
Philosophers like Berkeley questioned the reality of infinitesimal extensions versus tangible objects, leading to deep discussions in metaphysics.
In discussions about the continuum, infinitesimals challenge traditional views of divisibility in both mathematics and philosophy.

Pop Culture

The term often appears in science fiction, where fantastical concepts revolve around the manipulation of tiny particles or forces.
In literature, authors sometimes use infinitesimal as a metaphor for the small things that make a big difference in life.
Films and shows about quantum physics frequently reference the idea of infinitesimals, portraying realities that exist beyond human perception.

Translations

Translations of the word "infinitesimal" in other languages:

🇵🇹 infinitesimal

🇮🇳 अत्यल्प

🇩🇪 unendlich klein

🇮🇩 sangat kecil

🇺🇦 нескінченно малий

🇵🇱 nieskończenie mały

🇯🇵 無限小

🇫🇷 infinitésimal

🇪🇸 infinitesimal

🇹🇷 sonsuz küçük

🇰🇷 극소의

🇸🇦 ضئيل للغاية

🇨🇿 nekonečně malý

🇸🇰 nekonečne malý

🇨🇳 无限小

🇸🇮 neskončno majhen

🇮🇸 óendanlega lítill

🇰🇿 шексіз шағын

🇬🇪 უსაზღვროდ მცირე

🇦🇿 sonsuz kiçik

🇲🇽 infinitesimal

Word Frequency Rank

With rank #16,160, this word belongs to specialized vocabulary. While not common in everyday speech, it enriches your ability to express complex ideas.

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16157 diagonally
16158 bouncing
16159 armchair
16160 infinitesimal
16161 loser
16162 foresaw
16163 laryngeal
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