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disjoint – equilateral triangle
disjoint
Two sets are disjoint if they have empty intersection.
disjoint union
A union of sets which are disjoint.
disk
A set of points consisting of a circle together with its interior points. The set consisting only of the interior points of a circle is called an open disk.
Cf. neighborhood.
distance
The distance between two points in a space is given by the length of the geodesic joining those two points. In Euclidean space, the geodesic is given by a straight line, and the distance between two points is the length of this line. The distance between two points a and b on a real number line is the absolute value of their difference, i.e., d(a, b) = |a - b|. In two (or more) dimensions, the distance is given by the (generalized) Pythagorean theorem, i.e., in a Cartesian coordinate system of n dimensions, where a = (a1, ... ,an) and b = (b1, ... ,bn), the distance d(a, b) is given by
The concept of distance may be generalized to more abstract spaces – such a distance concept is referred to as a metric.
Graph Theory: The length of the shortest path between two vertices of a graph. If there is no path between two vertices, their distance is defined to be infinite. The distance between two vertices v and u is denoted by d(v, u). In a connected graph, distance is a metric.
distributive
See distributive property.
distributive lattice
A lattice is called distributive if for all elements x, y, and z of the lattice we have x  (y  z) = (x y) (x z) and x (y z) = (x y) (x z).
distributive property
An algebraic property of numbers which states that for all numbers a, b, and c, a(b + c) = ab + ac.
Cf. commutative, associative.
divide
To divide a number a by another number b is to find a third number c such that the product of b and c is a, that is, b × c = a. The number a is called the dividend, the number b is called the divisor, and the number c is called the quotient. The operation of dividing may be denoted by a horizontal or diagonal slash separating the dividend and divisor (with the dividend on top), or by a horizontal dash with a dot above and below it placed between the dividend and divisor.
In the case of whole numbers a and b there may not be a whole number quotient; however, there are always unique whole numbers q and r such that a = b × q + r, with r < b. In this case q is called the quotient and r is called the remainder. If in a particular case r = 0, we say that b divides a, and this is often denoted by b|a.
dividend
A number that is being divided.
divisor
A number that is dividing another.
dodecahedron
A polyhedron having twelve faces.
The faces of a regular dodecahedron are regular pentagons.
Cf. Platonic solid.
domain
General: A universe of discourse, that is, the class of objects under consideration. Functions and relations: The domain of a function (relation) is the set of elements which the function (relation) maps to its range set.
e
See Euler number.
edge
General: A line formed by the intersection of two planes. In a 3-dimensional figure (such as a polyhedron), the line or curve where two faces or surfaces meet.
Graph Theory: One of two kinds of entities in a graph. Restricted to being incident on exactly two vertices.
edge set
The set of edges of some graph. For a graph G, the edge set of G is denoted by E(G), or, if there is no ambiguity as to the graph in question, simply by E.
ellipse
The locus of points in the plane, the sum of whose distances from two fixed points, called the foci, remains constant.
Like the hyperbola and parabola, the ellipse is a conic section.
Related article: Conics
empty set
The unique set having no elements, generally denoted by a circle with a forward slash through it, or by an empty pair of braces.
Epimenides Paradox
See Liar Paradox.
epimorphism
A morphism f from X to Y is called an epimorphism when it is surjective, that is, when to each element y of Y there corresponds an x in X such that f(x) = y.
Cf. monomorphism.
equicontinuous
Let C[a,b] denote the space of all continuous functions on the real interval [a,b]. A subset S of C[0,1] is called equicontinuous at x in [a,b] if for any e greater than zero there is some d greater than zero such that for every function f in S we have:
equilateral triangle
A triangle with equal sides and equal angles.
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