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  2. Cartesian product - Wikipedia

    en.wikipedia.org/wiki/Cartesian_product

    A table can be created by taking the Cartesian product of a set of rows and a set of columns. If the Cartesian product rows × columns is taken, the cells of the table contain ordered pairs of the form (row value, column value). [4] One can similarly define the Cartesian product of n sets, also known as an n-fold Cartesian product, which can be ...

  3. Product topology - Wikipedia

    en.wikipedia.org/wiki/Product_topology

    In topology and related areas of mathematics, a product space is the Cartesian product of a family of topological spaces equipped with a natural topology called the product topology. This topology differs from another, perhaps more natural-seeming, topology called the box topology , which can also be given to a product space and which agrees ...

  4. List of set identities and relations - Wikipedia

    en.wikipedia.org/wiki/List_of_set_identities_and...

    A universe set is an absorbing element of binary union . The empty set is an absorbing element of binary intersection and binary Cartesian product , and it is also a left absorbing element of set subtraction :

  5. Product (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Product_(mathematics)

    In set theory, a Cartesian product is a mathematical operation which returns a set (or product set) from multiple sets. That is, for sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b) —where a ∈ A and b ∈ B. [5] The class of all things (of a given type) that have Cartesian products is called a Cartesian ...

  6. Ordered pair - Wikipedia

    en.wikipedia.org/wiki/Ordered_pair

    The set of all ordered pairs whose first entry is in some set A and whose second entry is in some set B is called the Cartesian product of A and B, and written A × B. A binary relation between sets A and B is a subset of A × B. The (a, b) notation may be used for other purposes, most notably as denoting open intervals on the real number line ...

  7. Algebra of sets - Wikipedia

    en.wikipedia.org/wiki/Algebra_of_sets

    The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".

  8. Function (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Function_(mathematics)

    The set of all these pairs is called the Cartesian product of X and Y and denoted . Thus, the above definition may be formalized as follows. A function with domain X and codomain Y is a binary relation R between X and Y that satisfies the two following conditions: [ 10 ]

  9. Baire space (set theory) - Wikipedia

    en.wikipedia.org/wiki/Baire_space_(set_theory)

    The Baire space is defined to be the Cartesian product of countably infinitely many copies of the set of natural numbers, and is given the product topology (where each copy of the set of natural numbers is given the discrete topology). The Baire space is often represented using the tree of finite sequences of natural numbers.