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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 set R union {infty}, obtained by adjoining one improper element to the set R of real numbers, is the set of projectively extended real numbers. Although notation is not ...

The supremum is the least upper bound of a set S, defined as a quantity M such that no member of the set exceeds M, but if epsilon is any positive quantity, however small, ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...

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 ...

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 ...

A vertex cut, also called a vertex cut set or separating set (West 2000, p. 148), of a connected graph G is a subset of the vertex set S subset= V(G) such that G-S has more ...

Two sets A_1 and A_2 are disjoint if their intersection A_1 intersection A_2=emptyset, where emptyset is the empty set. n sets A_1, A_2, ..., A_n are disjoint if A_i ...

In the theory of transfinite ordinal numbers, 1. Every well ordered set has a unique ordinal number, 2. Every segment of ordinals (i.e., any set of ordinals arranged in ...