cartesian product Synonyms
No Synonyms and anytonyms found
cartesian product Meaning
Wordnet
cartesian product (n)
the set of elements common to two or more sets
cartesian product Sentence Examples
- In set theory, the cartesian product of two sets A and B, denoted as A × B, is the set of all possible ordered pairs (a, b) where a is from set A and b is from set B.
- The cartesian product is a fundamental concept in mathematics, providing a systematic way to combine elements from different sets.
- For example, if set A = {1, 2} and set B = {x, y}, then the cartesian product A × B would be {(1, x), (1, y), (2, x), (2, y)}.
- The cartesian product allows us to analyze relationships between elements of different sets and construct new sets based on those relationships.
- Cartesian products are not limited to pairs of sets; they can be extended to any finite or infinite number of sets.
- The concept of cartesian product is widely used in various branches of mathematics, including algebra, topology, and combinatorics.
- In relational databases, cartesian products can occur unintentionally when joining tables without specifying a condition.
- Understanding cartesian products is crucial for solving problems involving permutations, combinations, and probability.
- The cartesian product of sets A, B, and C, denoted as A × B × C, represents the set of all possible ordered triples (a, b, c) where a is from set A, b is from set B, and c is from set C.
- The cartesian product provides a powerful framework for exploring the relationships between elements of different sets and is a cornerstone of many mathematical concepts and applications.
FAQs About the word cartesian product
the set of elements common to two or more sets
No synonyms found.
No antonyms found.
In set theory, the cartesian product of two sets A and B, denoted as A × B, is the set of all possible ordered pairs (a, b) where a is from set A and b is from set B.
The cartesian product is a fundamental concept in mathematics, providing a systematic way to combine elements from different sets.
For example, if set A = {1, 2} and set B = {x, y}, then the cartesian product A × B would be {(1, x), (1, y), (2, x), (2, y)}.
The cartesian product allows us to analyze relationships between elements of different sets and construct new sets based on those relationships.
