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A set partition of a set S is a collection of disjoint subsets of S whose union is S. The number of partitions of the set {k}_(k=1)^n is called a Bell number.

A set having exactly one element a. A singleton set is denoted by {a} and is the simplest example of a nonempty set.

A set S with a single point P removed is called a punctured set, written S\{P}.

Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all ...

A degree set is a set of integers that make up a degree sequence. Any set of positive integers is the degree set for some graph, because any odd integer from that set can be ...

The concept of irredundance was introduced by Cockayne et al. (1978). Let N_G[v] denote the graph neighborhood of a vertex v in a graph G (including v itself), and let N_G[S] ...

There are several equivalent definitions of a closed set. Let S be a subset of a metric space. A set S is closed if 1. The complement of S is an open set, 2. S is its own set ...

A countable set is a set that is either finite or denumerable. However, some authors (e.g., Ciesielski 1997, p. 64) use the definition "equipollent to the finite ordinals," ...

The arc set of a directed graph is the set of all arcs (directed edges) of the graph. The arc set for a directed graph g is given in the Wolfram Language by EdgeList[g].

The set difference A\B is defined by A\B={x:x in A and x not in B}. Here, the backslash symbol is defined as Unicode U+2216. The set difference is therefore equivalent to the ...