Infinitesimal: meaning, definitions and examples

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infinitesimal

 

[ ɪnˌfɪnɪˈtɛsɪməl ]

Adjective / Noun
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.

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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.

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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?

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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.

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

Etymology

The term 'infinitesimal' originated in the late 17th century from the Latin words 'infinitus' (unbounded) and 'esimal' (from 'exiguus,' meaning small). It was introduced by mathematicians to describe quantities that are smaller than any finite quantity but not zero. The concept of infinitesimals played a significant role in the development of calculus by mathematicians like Newton and Leibniz, leading to a revolution in mathematical analysis and the understanding of limits and derivatives.

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.