The phrase "mapping onto itself" is primarily used as a verb phrase in a technical or academic context, particularly in mathematics and computer science.
/mæpɪŋ ˈɒntuː ɪtˈsɛlf/
"Mapping onto itself" refers to the process where a function or relation takes an input from a set and produces an output that is an element of the same set. This concept is often discussed in the fields of mathematics, particularly in set theory and functions, as well as in computer science, especially in discussions on algorithms and data structures.
This phrase is not commonly used in everyday conversation and is predominantly found in written academic or technical texts. It would typically appear in scholarly articles, textbooks, or technical documentation.
Функция определена таким образом, что каждый элемент в множестве отображается на себя, что обеспечивает тождественное преобразование.
In set theory, a bijective function guarantees that each input is mapping onto itself uniquely.
В теории множеств биективная функция гарантирует, что каждый ввод уникально отображается на себя.
The properties of the matrix demonstrate that it is mapping onto itself, reflecting its symmetrical nature.
The phrase "mapping onto itself" is specific to certain contexts and doesn’t form idiomatic expressions in everyday English; however, the notion of "mapping" can appear in various idiomatic uses. The following phrases incorporate the concept of mapping in broader expressions.
"Простраивать план" часто относится к тщательному планированию стратегии.
"Map the landscape" describes understanding the situation before making decisions.
"Картировать ландшафт" описывает понимание ситуации перед принятием решений.
"Map something to something" means to correlate one aspect with another.
"Соотнести что-то с чем-то" означает коррелировать один аспект с другим.
"Take the map as a guide" suggests using guidance to navigate a situation.
The word "mapping" derives from "map," which traces its origins back to the early 14th century, from the Latin "mappa," meaning "napkin" or "cloth," as maps were originally drawn on cloth. The term "itself" is a combination of "it" and "self," indicating something is referring to its own being, and has Old English roots.
This provides a comprehensive overview of the phrase "mapping onto itself," highlighting its academic significance, usage, and related linguistic components.