Noun Phrase
/lɑrdʒ sɪv ɪnɪˈkwaɪəti/
The "large sieve inequality" refers to a mathematical result in number theory, particularly in analytic number theory. It is a tool used to estimate the size of sets of numbers that possess certain properties, especially those relating to prime numbers and their distribution. This inequality is essential for various results in sieves, particularly large sieve methods which are used to exploit the distribution of primes.
The term "large sieve inequality" is primarily used in academic and mathematical contexts. It is more common in written form, especially in research papers, textbooks, and lectures related to number theory and analytic methods.
Translation: Неравенство большого сита предоставляет рамки для оценки числа простых чисел в определенных интервалах.
By applying the large sieve inequality, researchers were able to obtain bounds on the prime counting functions.
Translation: Применяя неравенство большого сита, исследователи смогли получить границы для функций подсчета простых чисел.
The large sieve inequality has proven instrumental in advancing our understanding of prime gaps.
While the term "large sieve inequality" itself is quite technical and not widely recognized outside of mathematics, the concept of "sieve" appears in several idiomatic expressions related to filtering or separating.
Translation: "Пусть плохие яблоки пройдут через сито."
"Time will sift through all the lies like a sieve."
Translation: "Время просеет все лжи, как через сито."
"She used a sieve to filter out the unnecessary noise."
Translation: "Она использовала сито, чтобы отфильтровать ненужный шум."
"His stories became truth only after passing through the sieve of scrutiny."
Translation: "Его истории стали правдой только после того, как прошли через сито критики."
"We need to sieve through these applications to find the best candidates."
The term "sieve" comes from the Old English word "sife," which means "to sift" or "to separate." The adjective "large" indicates the scale or extent of the sieve being referred to, implying that it is designed to capture or estimate large sets of numbers.
This structure provides a comprehensive overview of the term "large sieve inequality," highlighting its significance in mathematics while also contextualizing the concept in everyday language.