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If x is a member of a set A, then x is said to be an element of A, written x in A. If x is not an element of A, this is written x not in A. The term element also refers to a ...

The ascending chain condition, commonly abbreviated "A.C.C.," for a partially ordered set X requires that all increasing sequences in X become eventually constant. A module M ...

A topological basis is a subset B of a set T in which all other open sets can be written as unions or finite intersections of B. For the real numbers, the set of all open ...

Given a set P of primes, a field K is called a class field if it is a maximal normal extension of the rationals which splits all of the primes in P, and if P is the maximal ...

Let a graph G=(V,E) be defined on vertex set V and edge set E. Then a construction sequence (or c-sequence) for G is a linear order on V union E in which each edge appears ...

The mode of a set of observations is the most commonly occurring value. For example, for a data set (3, 7, 3, 9, 9, 3, 5, 1, 8, 5) (left histogram), the unique mode is 3. ...

The Cartesian product of two sets A and B (also called the product set, set direct product, or cross product) is defined to be the set of all points (a,b) where a in A and b ...

From the point of view of coordinate charts, the notion of tangent space is quite simple. The tangent space consists of all directions, or velocities, a particle can take. In ...

In geometry, the term "enlargement" is a synonym for expansion. In nonstandard analysis, let X be a set of urelements, and let V(X) be the superstructure with individuals in ...

One of the Zermelo-Fraenkel axioms, also known as the axiom of regularity (Rubin 1967, Suppes 1972). In the formal language of set theory, it states that x!=emptyset=> exists ...