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A subset E of a topological space S is said to be of first category in S if E can be written as the countable union of subsets which are nowhere dense in S, i.e., if E is ...

There are a number of meanings for the word "arc" in mathematics. In general, an arc is any smooth curve joining two points. The length of an arc is known as its arc length. ...

The nesting of two or more functions to form a single new function is known as composition. The composition of two functions f and g is denoted f degreesg, where f is a ...

Define the abundancy Sigma(n) of a positive integer n as Sigma(n)=(sigma(n))/n, (1) where sigma(n) is the divisor function. Then a pair of distinct numbers (k,m) is a ...

A path in a graph G is a subgraph of G that is a path graph (West 2000, p. 20). The length of a path is the number of edges it contains. In most contexts, a path must contain ...

In combinatorial logic minimization, a device known as a Karnaugh map is frequently used. It is similar to a truth table, but the various variables are represented along two ...

The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x = ...

A simple directed graph is a directed graph having no multiple edges or graph loops (corresponding to a binary adjacency matrix with 0s on the diagonal). The number of simple ...

"The" square graphs is the cycle graph C_4. It is isomorphic to the complete bipartite graph K_(2,2). Like all cycle graphs, the line graph of C_4 is isomorphic to itself. A ...

Let A and B be any sets. Then the product of |A| and |B| is defined as the Cartesian product |A|*|B|=|A×B| (Ciesielski 1997, p. 68; Dauben 1990, p. 173; Moore 1982, p. 37; ...