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The (upper) vertex independence number of a graph, often called simply "the" independence number, is the cardinality of the largest independent vertex set, i.e., the size of ...

The set of elements belonging to one but not both of two given sets. It is therefore the union of the complement of A with respect to B and B with respect to A, and ...

The union of two sets A and B is the set obtained by combining the members of each. This is written A union B, and is pronounced "A union B" or "A cup B." The union of sets ...

The set of all nonsingular affine transformations of a translation in space constitutes a group known as the affine group. The affine group contains the full linear group and ...

Let P be the set of primes, and let Q_p and Z_p(t) be the fields of p-adic numbers and formal power series over Z_p=(0,1,...,p-1). Further, suppose that D is a "nonprincipal ...

The conjecture proposed by Catalan in 1888 and extended by E. Dickson that each aliquot sequence ends in a prime, a perfect number, or a set of sociable numbers. The ...

A Cevian point P is point with respect to which a set of Cevians of a triangle are taken. Connecting the endpoints of the Cevians through a point P gives the so-called Cevian ...

Consider a set of points X_i on an attractor, then the correlation integral is C(l)=lim_(N->infty)1/(N^2)f, where f is the number of pairs (i,j) whose distance |X_i-X_j|<l. ...

A discrete space is simply a topological space equipped with the discrete topology. A discrete space is always a metric space, namely the metric space with the same ...

If X is a normed linear space, then the set of continuous linear functionals on X is called the dual (or conjugate) space of X. When equipped with the norm ...