Infinitesimal: meaning, definitions and examples
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infinitesimal
[ ɪnˌfɪnɪˈtɛsɪməl ]
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
Which Synonym Should You Choose?
Word | Description / Examples |
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infinitesimal |
Used in scientific and mathematical contexts to describe extremely small quantities or sizes.
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tiny |
Commonly used in everyday language to describe something very small, often in an informal or general context.
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minuscule |
Used to describe something that is very small in size but not necessarily microscopic or scientific in nature.
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microscopic |
Applied when discussing objects or organisms that are so small they can only be seen with a microscope.
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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.
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 |
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infinitesimal |
Used in mathematical or scientific contexts to describe something extremely small or approaching zero.
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microscopic quantity |
Used in scientific contexts, particularly in biology, chemistry or physics, to describe quantities or objects that require a microscope to be seen.
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infinitely small value |
Used in general contexts to describe something very small, especially in mathematics, often to emphasize the extremely small size.
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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.
general
In everyday language, infinitesimal can refer to something extremely small or insignificant.
Synonyms
Which Synonym Should You Choose?
Word | Description / Examples |
---|---|
infinitesimal |
Used in a scientific or mathematical context to describe something extremely small, almost approaching zero.
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negligible |
Indicates that something is so small or unimportant that it can be disregarded, often used in both technical and everyday contexts.
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minimal |
Describes something that is the smallest in amount or degree, often in everyday situations, and does not imply a scientific context.
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trivial |
Used to describe something that is very small or unimportant, often in a context that suggests it is not worth considering.
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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.