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(Поясним, что its означает “the one (ones) belonging to it.” Стало быть, its singular point = the singular point of it. Разумеется, это не отменяет правила “ every can co-occur with possessives” (R. Quirk et al.) и, скажем, как уже отмечалось, its every subalgebra = each of its subalgebras.) In English “respectively” is seldom inserted in the second parenthesis, and in general the word “respectively” is used far less often in English than in Russian. The Russian word пункт means “item,” “heading” or “subsection,” usually numbered; параграф means “section”; the Russian word for “paragraph” is абзац. When работа refers to a definite book or article, the translation “work” is sometimes unidiomatic; работа should then be translated by “book” or “article,” depending on which of the two it actually is; but often it can be simply omitted. It is a solecism in English to use the word “both,” instead of “the two,” in a statement which, usually because of the presence of some word like “together” or “equal,” becomes nonsensical when applied to one person or thing. Thus “the numbers are both large” but “the two numbers are equal.” There is no such limitation on the Russian word оба. It is true that in English “may” is sometimes more elegant than “can”; for example, “we may assume that n is prime.” But “can” is much safer, especially with such words as “not” and “only.” “May not” is ambiguous in English.... In Russian there are many variants for “if and only if,”... but the phrase does not vary in English. (Запомните, что математическая новация iff уже много лет встречается в хороших книгах, и у Вас есть известные основания при необходимости ее использовать. Излишнюю для нужд эпизодического перевода элегантность создает (необязательная) пунктуация ...if, and only if,...!) The combination “since ..., then ...” (так как ..., то ...) is extremely common in mathematical Russian but totally inadmissible in English. When a signpost is needed in English ... to show where the principal clause begins, the best one is usually “it follows that,” and if this phrase seems too ponderous, the translation can fall back on the stereotyped “we have.” 110
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