Part of Speech

• Noun

Phonetic Transcription

• /kɑːˈteɪ.ʒən mʌl.tɪˈplɪ.keɪ.ʃən/

Meaning

Cartesian multiplication refers to a mathematical operation that produces a Cartesian product of two sets. In set theory, the Cartesian product of two sets A and B is a set of ordered pairs, where the first element of each pair comes from A and the second element comes from B.

Usage

Cartesian multiplication is commonly used in mathematics, especially in set theory, database theory, and computer science. It is a fundamental concept when dealing with relations and functions in a mathematical or logical context. The term is more frequently used in written contexts, particularly in academic texts, research papers, and lectures.

Frequency of Use

Cartesian multiplication is not used in everyday conversation; it is primarily a technical term found in academic and professional language.

Example Sentences

1. "In mathematics, the Cartesian multiplication of sets A and B will yield the set of ordered pairs (a, b) where a ∈ A and b ∈ B."

2. "В математике Картиесианское умножение множеств A и B даст множество упорядоченных пар (a, b), где a ∈ A и b ∈ B."

3. "To understand the concept better, we can visualize the Cartesian multiplication of two finite sets."

4. "Чтобы лучше понять концепцию, мы можем визуализировать Картиесианское умножение двух конечных множеств."

5. "Cartesian multiplication is essential for defining relations in a multi-dimensional space."

6. "Картиесианское умножение необходимо для определения отношений в многомерном пространстве."

Idiomatic Expressions

"Cartesian multiplication" itself is not commonly used in idiomatic expressions; however, the concepts underlying Cartesian multiplication can appear in mathematical idioms or expressions related to functions and relationships.

Example Sentences with Related Concepts

1. "To determine the final outcome, we need to consider all the combinations that arise from the Cartesian product."

2. "Чтобы определить конечный результат, нам нужно рассмотреть все комбинации, которые возникают из Картиесианского произведения."

3. "The data analysis utilized Cartesian multiplication to derive new relationships between variables."

4. "Анализ данных использовал Картиесианское умножение для вывода новых отношений между переменными."

5. "She explained how to perform Cartesian multiplication to establish connections between different datasets."

6. "Она объяснила, как выполнять Картиесианское умножение, чтобы установить связи между различными наборами данных."

7. "Using Cartesian multiplication, researchers can visualize all possible interactions in their model."

8. "Используя Картиесианское умножение, исследователи могут визуализировать все возможные взаимодействия в своей модели."

Etymology

The term "Cartesian" is derived from the name of the French philosopher and mathematician René Descartes, who developed a coordinate system that laid the groundwork for analytic geometry. "Multiplication" comes from the Latin word "multiplicatio," meaning "the act of multiplying." Combined, "Cartesian multiplication" signifies the multiplication of sets in the context of Descartes' coordinate system.

Synonyms and Antonyms

Synonyms

• Cartesian product
• Cross product (in vector context)

Antonyms

• Disjoint sets (in terms of relationship; not directly applicable to multiplication but opposite in set inclusion)