## biconnected graph

Overview page. Subjects: Computing.

A graph *G*, either directed or undirected, with the property that for every three distinct vertices *u*, *v*, and *w* there is a path from *u* to *w* not containing *v*. For an undirected graph, this is...

## common denominator

Overview page. Subjects: Mathematics.

An integer that is exactly divisible by all the denominators of a group of fractions. Used in adding or subtracting where the first step is to express each fraction as an equivalent...

## component

Overview page. Subjects: Mathematics.

(of a graph)

A graph may be ‘in several pieces’ and these are called its components: two vertices are in the same component if and only if there is a path from one to the other. A...

## congruence

Overview page. Subjects: Mathematics.

(modulo *n*)

For each positive integer *n*, the relation of congruence between integers is defined as follows: *a* is congruent to *b* modulo *n* if *a*−*b* is a multiple of *n*. This is written *a*null...

## congruence relation

Overview page. Subjects: Computing.

*m* be some given but fixed positive integer and let *a* and *b* be arbitrary integers. Then *a* is...

## equivalence class

Overview page. Subjects: Computing.

A subset of a set *S* (on which an equivalence relation is defined) that consists of all the elements of *S* that are equivalent to each other, and to no other elements of *S*. An equivalence...

## Myhill equivalence

Overview page. Subjects: Computing.

An equivalence relation arising in formal language theory. If *L* is a language over alphabet Σ (see word) then its Myhill equivalence is the relation =M on Σ* defined as follows:

null...

## Nerode equivalence

Overview page. Subjects: Computing.

An equivalence relation, =_{N}, arising in formal language theory. It is defined analogously to the Myhill equivalence by the weaker properties:

for a language *L* over Σ, *u* =_{N}null...

## ordering relation

Overview page. Subjects: Philosophy.

A partial ordering on a set is a relation < that is transitive and reflexive and antisymmetric. That is, *x* < *y* & *y* < *z* → *x* < *z*; *x* < *x*; *x* < *null...*

## partition

Overview page. Subjects: Mathematics.

(of a positive integer)

A partition of the positive integer *n* is obtained by writing *n*=*n*
_{1}+*n*
_{2}+…+*n*
_{
k
}, where *n*null...

## rational number

Overview page. Subjects: Mathematics.

Any number that can be expressed as the ratio of two integers. For example, 0.3333… is rational because it can be written as 1/3. √2, however, is an irrational number.

## relation

Overview page. Subjects: Computing.

A relation on a set *S* is usually a binary relation on *S*, though the notion can be extended to involve more than two elements. An example of a ternary relation, involving three elements, is ‘*null...*

## relation

Overview page. Subjects: Philosophy.

Philosophically relations are interesting because of the historic prejudice, given its most forceful expression by Leibniz, that they are somehow ‘unreal’ compared to the intrinsic, monadic...

## representative

Overview page. Subjects: Mathematics.

Given an equivalence relation on a set, any one of the equivalence classes can be specified by giving one of the elements in it. The particular element *a* used can be called a representative...

## residue class

Overview page. Subjects: Mathematics.

(modulo n)

An equivalence class for the equivalence relation of congruence modulo *n*. So, two integers are in the same class if they have the same remainder upon division by *n*. If [*a*null...