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Let (,) and (,) be ordered pairs. Then the characteristic (or defining) property of the ordered pair is: (,) = (,) = =.. 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.
Lattices, partial orders in which each pair of elements has a greatest lower bound and a least upper bound. Many different types of lattice have been studied; see map of lattices for a list. Partially ordered sets (or posets), orderings in which some pairs are comparable and others might not be
This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes.
A partially ordered set (poset for short) is an ordered pair = (,) consisting of a set (called the ground set of ) and a partial order on . When the meaning is clear from context and there is no ambiguity about the partial order, the set X {\displaystyle X} itself is sometimes called a poset.
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
The set of all ordered pairs obtained from two sets, where each pair consists of one element from each set. cardinal 1. A cardinal number is an ordinal with more elements than any smaller ordinal cardinality The number of elements of a set categorical 1. A theory is called categorical if all models are isomorphic. This definition is no longer ...
A 1‑tuple is called a single (or singleton), a 2‑tuple is called an ordered pair or couple, and a 3‑tuple is called a triple (or triplet). The number n can be any nonnegative integer . For example, a complex number can be represented as a 2‑tuple of reals, a quaternion can be represented as a 4‑tuple, an octonion can be represented as ...
7 Relative to the real/complex numbers. ... List of set identities and relations – Equalities for combinations of sets; List of types of functions This page was ...