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A totally ordered set (A,<=) is said to be well ordered (or have a well-founded order) iff every nonempty subset of A has a least element (Ciesielski 1997, p. 38; Moore 1982, ...

Let G be a group of group order h and D be a set of k elements of G. If the set of differences d_i-d_j contains every nonzero element of G exactly lambda times, then D is a ...

The formal term used for a collection of objects. It is denoted {a_i}_(i in I) (but other kinds of brackets can be used as well), where I is a nonempty set called the index ...

One of the most useful tools in nonstandard analysis is the concept of a hyperfinite set. To understand a hyperfinite set, begin with an arbitrary infinite set X whose ...

"Aggregate" is an archaic word for infinite sets such as those considered by Georg Cantor. The term is sometimes also used to refer to a finite or infinite set in which ...

The axiom of Zermelo-Fraenkel set theory which asserts the existence for any set a of the sum (union) x of all sets that are elements of a. The axiom may be stated ...

A set of maximum degree to which all other degrees of recursively enumerable sets can be many-one reduced. If set A is many-one complete, then it is one-one complete, and ...

A set of maximum degree to which all other degrees of recursively enumerable sets can be one-one reduced. If set A is many-one complete, then it is one-one complete, and vice ...

An outer measure mu on R^n is Borel regular if, for each set X subset R^n, there exists a Borel set B superset X such that mu(B)=mu(X). The d-dimensional Hausdorff outer ...

Giving a set F={f_1,f_2,...,f_n} of contracting similitudes of R^l, the closed set E is said to be subselfsimilar for F if E subset union _(i=1)^nf_i(E) (Falconer 1995, ...