Russian Translation(s) & Details for 'infinitesimally'

English Word: infinitesimally

Key Russian Translations:

• бесконечно малым [bʲɪsˈkɐnʲɪt͡ɕnə mɐˈlɨm] - [Formal, used in scientific or mathematical contexts]

Frequency: Low (Primarily used in technical, scientific, or academic discussions; not common in everyday conversation)

Difficulty: Advanced (C1 level; requires understanding of advanced grammar and vocabulary in Russian, especially for abstract concepts)

Pronunciation (Russian):

бесконечно малым: [bʲɪsˈkɐnʲɪt͡ɕnə mɐˈlɨm]

Note on бесконечно малым: The stress falls on the third syllable of "бесконечно" [kɐnʲɪt͡ɕnə]. This phrase combines an adverb and an adjective in the instrumental case, which can be challenging for learners due to its compound structure.

Audio: []

Meanings and Usage:

Meaning 1: In an infinitely small or negligible manner, often in scientific or mathematical contexts.

Translation(s) & Context:

• бесконечно малым - Used in formal descriptions of quantities that approach zero, such as in calculus or physics.

Usage Examples:

• В математическом анализе величина изменяется бесконечно малым образом.

  In mathematical analysis, the quantity changes infinitesimally.

• Эта частица движется бесконечно малым шагом по оси координат.

  This particle moves infinitesimally along the coordinate axis.

• В квантовой механике энергия может увеличиваться бесконечно малым количеством.

  In quantum mechanics, energy can increase by an infinitesimally small amount.

• Процесс эволюции происходит бесконечно малым темпом в геологических масштабах.

  The process of evolution occurs at an infinitesimally slow pace on geological scales.

• Давление в системе снижается бесконечно малым градиентом.

  The pressure in the system decreases by an infinitesimally small gradient.

Russian Forms/Inflections:

"бесконечно малым" is a phrase combining the adverb "бесконечно" (unchanging in form as it is an adverb) and the adjective "малым" (instrumental singular masculine/neuter form of "малый"). Adjectives in Russian inflect based on case, number, and gender. "Малый" follows the standard first-declension pattern for adjectives.

Note: "Бесконечно" does not inflect and remains constant, while "малым" changes as shown. For other forms, adapt based on context (e.g., if used with different genders or numbers).

Russian Synonyms/Antonyms:

• Synonyms:
  • минимально [mʲɪˈnʲimɐlnə] - More general, used for very small changes.
  • незначительно [nʲɪznɐˈt͡ɕnə] - Implies something insignificant, with a subtle difference in connotation.
• Antonyms:
  • бесконечно большим [bʲɪsˈkɐnʲɪt͡ɕnə bɐlʲʂɪm] - Directly opposite, meaning infinitely large.
  • значительно [znɐˈt͡ɕnə] - Meaning significantly or substantially.

Related Phrases:

• Бесконечно малый интервал - An infinitesimally small interval; used in discussions of limits in mathematics.
• Изменяться на бесконечно малую величину - To change by an infinitesimally small amount; common in physics contexts.
• Бесконечно малый элемент - An infinitesimal element; refers to basic units in calculus or integration.

Usage Notes:

This translation corresponds closely to the English adverb "infinitesimally," emphasizing extreme smallness in quantitative contexts. In Russian, it's typically used in formal or technical writing, such as scientific papers, and requires the instrumental case for "малым" to indicate the manner of change. When choosing between synonyms like "минимально," opt for "бесконечно малым" in precise mathematical scenarios for accuracy. Be mindful of word order in sentences, as Russian often places the adverbial phrase at the end for emphasis.

Common Errors:

• Error: Using the nominative form "малый" instead of the instrumental "малым," e.g., saying "изменяется бесконечно малый" instead of "изменяется бесконечно малым."
  Correct: "Изменяется бесконечно малым" means "changes infinitesimally." Explanation: The instrumental case is required to express the means or manner, which English learners often overlook due to the lack of cases in English.
• Error: Confusing it with "бесконечно большой" (infinitely large), leading to antonym misuse.
  Correct: Ensure context demands smallness; for example, use "бесконечно малым" in limits, not in descriptions of growth. Explanation: This mix-up arises from similar adverbial structures, so double-check the root adjective.

Cultural Notes:

In Russian scientific literature, terms like "бесконечно малым" reflect the influence of Western mathematics, particularly from the 19th-century developments in calculus by figures like Lobachevsky. This phrase embodies the precision valued in Russian academic traditions, where exactness in language mirrors the rigor of scientific inquiry.

Related Concepts:

• лимит [lʲɪˈmʲit] - Limit (mathematical concept)
• дифференциал [dʲɪfʲɪˈrɛnʦʲiəl] - Differential
• интеграл [ʲɪnʲtʲɪˈɡrəl] - Integral