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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 ...

A maximal independent set is an independent set which is a maximal set, i.e., an independent set that is not a subset of any other independent set. The generic term "maximal ...

A maximum irredundant set is an irredundant set of largest possible size in a graph. Note that a maximum irredundant set is not equivalent to a maximal irredundant set, which ...

A class is a generalized set invented to get around Russell's antinomy while retaining the arbitrary criteria for membership which leads to difficulty for sets. The members ...

The definition of a set by enumerating its members. An extensional definition can always be reduced to an intentional one. An extension field is sometimes also called simply ...

The level set of a differentiable function f:R^n->R corresponding to a real value c is the set of points {(x_1,...,x_n) in R^n:f(x_1,...,x_n)=c}. For example, the level set ...

Two sets A and B are said to be independent if their intersection A intersection B=emptyset, where emptyset is the empty set. For example, {A,B,C} and {D,E} are independent, ...

A minimum dominating set is a dominating set of smallest size in a given graph. The size of a minimum dominating set is known as the domination number of the graph. A minimum ...

For a graph G and a subset S^t of the vertex set V(G), denote by N_G^t[S^t] the set of vertices in G which are adjacent to a vertex in S^t. If N_G^t[S^t]=V(G), then S^t is ...

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