Russian Translation(s) & Details for 'infinitesimal'

English Word: infinitesimal

Key Russian Translations:

• бесконечно малый [bʲɪsˈkonʲɪt͡ɕnə mɐˈlɨj] - [Formal, Mathematical context]

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

Difficulty: C1 (Advanced level, requiring familiarity with mathematical terminology and Russian adjective declensions)

Pronunciation (Russian):

бесконечно малый: [bʲɪsˈkonʲɪt͡ɕnə mɐˈlɨj]

Note on бесконечно малый: The stress falls on the third syllable of "бесконечно" and the second syllable of "малый." Be cautious with the palatalized 's' sound in "бесконечно," which is common in Russian adjectives. Variations may occur in rapid speech.

Audio: []

Meanings and Usage:

Meaning 1: Extremely small quantity, often in mathematical or scientific contexts

Translation(s) & Context:

• бесконечно малый - Used in formal mathematical discussions, such as calculus or physics, to describe quantities approaching zero without reaching it. Context: Academic writing or lectures.

Usage Examples:

• В математике бесконечно малые величины играют ключевую роль в дифференциальном исчислении.

  In mathematics, infinitesimal quantities play a key role in differential calculus.

• Ученые изучают бесконечно малые изменения в атомных структурах для понимания квантовой механики.

  Scientists study infinitesimal changes in atomic structures to understand quantum mechanics.

• В экономической модели бесконечно малый рост инфляции может привести к значительным долгосрочным эффектам.

  In the economic model, an infinitesimal growth in inflation can lead to significant long-term effects.

• Бесконечно малый угол поворота может быть критически важен в навигационных системах.

  An infinitesimal angle of rotation can be critically important in navigation systems.

• При анализе функций бесконечно малые приращения помогают определить производные.

  When analyzing functions, infinitesimal increments help determine derivatives.

Russian Forms/Inflections:

"Бесконечно малый" is an adjective in Russian and follows the standard adjective declension patterns. It is a compound adjective where "бесконечно" modifies "малый," but the entire phrase inflects as a single unit based on gender, number, and case.

Note: This follows regular adjective inflections. If used in a fixed phrase, it may remain invariant in certain contexts.

Russian Synonyms/Antonyms:

• Synonyms:
  • минимальный (minimal; often used in everyday contexts, with a slight nuance of being the smallest possible but not necessarily approaching zero)
  • незначительный (insignificant; implies lack of importance, differing from the precise mathematical sense of "infinitesimal")
• Antonyms:
  • бесконечно большой (infinitely large; used in contrasting mathematical concepts)
  • значительный (significant; opposite in scale and impact)

Related Phrases:

• бесконечно малые величины - Infinitesimal quantities; used in calculus to refer to values approaching zero.
• лимит бесконечно малых - Limit of infinitesimals; a concept in mathematical analysis.
• бесконечно малый анализ - Infinitesimal analysis; refers to the study of very small changes in functions.

Usage Notes:

"Бесконечно малый" directly corresponds to the English "infinitesimal" in mathematical contexts, emphasizing precision and formality. It is typically restricted to scientific or academic language; in casual conversation, Russians might opt for simpler terms like "очень маленький" to avoid complexity. When using this term, ensure agreement in gender, number, and case with the noun it modifies, as Russian adjectives must decline. For learners, choose this translation over synonyms when discussing exact mathematical concepts, but be aware that it may sound overly technical in non-specialized settings.

Common Errors:

• Error: Using "бесконечно малый" incorrectly in non-mathematical contexts, such as everyday descriptions (e.g., saying "бесконечно малый дом" for a very small house, which sounds awkward).

  Correct: Opt for "очень маленький дом" instead. Explanation: "Бесконечно малый" implies a theoretical limit, not just small size, so it can confuse native speakers if misapplied.

• Error: Failing to decline the adjective properly, e.g., using "бесконечно малый" in all cases regardless of the noun (e.g., "в бесконечно малый" instead of "в бесконечно малом").

  Correct: "В бесконечно малом количестве" (In an infinitesimal quantity). Explanation: Russian requires adjective-noun agreement; neglecting this makes the sentence grammatically incorrect.

Cultural Notes:

In Russian culture and education, terms like "бесконечно малый" are deeply rooted in the Soviet-era emphasis on mathematics and science. Russian mathematics education often introduces such concepts early, reflecting a historical focus on theoretical sciences during the Cold War, which may give the term a more precise, intellectual connotation compared to its English counterpart.

Related Concepts:

• лимит
• производная
• интеграл
• квантовая механика