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Transitivity is a result of the symmetry in the group. A group G is called transitive if its group action (understood to be a subgroup of a permutation group on a set Omega) ...

The minimum excluded value. The mex of a set S of nonnegative integers is the least nonnegative integer not in the set.

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 ...

A level set in three dimensions.

A series is an infinite ordered set of terms combined together by the addition operator. The term "infinite series" is sometimes used to emphasize the fact that series ...

Let (A,<=) be a well ordered set. Then the set {a in A:a<k} for some k in A is called an initial segment of A (Rubin 1967, p. 161; Dauben 1990, pp. 196-197; Moore 1982, pp. ...

A point which is a member of the set closure of a given set S and the set closure of its complement set. If A is a subset of R^n, then a point x in R^n is a boundary point of ...

A definition of a set by mentioning a defining property.

Let X be an infinite set of urelements, and let V(^*X) be an enlargement of V(X). Let H in V(^*X) be an algebra. Then H is hyperfinitely generated provided that it has a ...

A set in a Polish space is a Borel set iff it is both analytic and coanalytic. For subsets of w, a set is delta_1^1 iff it is "hyperarithmetic."