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Let R(z) be a rational function R(z)=(P(z))/(Q(z)), (1) where z in C^*, C^* is the Riemann sphere C union {infty}, and P and Q are polynomials without common divisors. The ...

A set S together with a relation >= which is both transitive and reflexive such that for any two elements a,b in S, there exists another element c in S with c>=a and c>=b. In ...

An ambiguous term which is sometimes used to mean a partially ordered set and sometimes to mean a totally ordered set.

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of ...

Given a set S with a subset E, the complement (denoted E^' or E^_) of E with respect to S is defined as E^'={F:F in S,F not in E}. (1) Using set difference notation, the ...

The edge set of a graph is simply a set of all edges of the graph. The cardinality of the edge set for a given graph g is known as the edge count of g. The edge set for a ...

The set containing no elements, commonly denoted emptyset or emptyset, the former of which is used in this work. These correspond to Wolfram Language and TeX characters ...

A set S and a binary operator * are said to exhibit closure if applying the binary operator to two elements S returns a value which is itself a member of S. The closure of a ...

Set theory is the mathematical theory of sets. Set theory is closely associated with the branch of mathematics known as logic. There are a number of different versions of set ...

Given n mutually exclusive events A_1, ..., A_n whose probabilities sum to unity, then P(B)=P(B|A_1)P(A_1)+...+P(B|A_n)P(A_n), where B is an arbitrary event, and P(B|A_i) is ...