BROWSE ALPHABETICALLY LEVEL:    Elementary    Advanced    Both INCLUDE TOPICS:    Basic Math    Algebra    Analysis    Biography    Calculus    Comp Sci    Discrete    Economics    Foundations    Geometry    Graph Thry    History    Number Thry    Phys Sci    Statistics    Topology    Trigonometry		convergent series – D-system convergent series   See series. Related article: Series converse relation   If R is a relation, the relation R´ is called the converse relation of R if whenever xRy we have yR´x. converse statement   Given a conditional, i.e., a statement of the form “if A then B,” or “A implies B,” its converse is “B implies A.” A conditional neither implies nor is implied by its converse. However, the converse of a conditional and its inverse are logically equivalent, since they are contrapositives of each other. convex   Naively, a region of space is convex if the line segement joining any two points of the region lies wholly within it. Thus, a polygon is convex if every line segment joining any two points on its sides lies entirely within the polygon. (This is equivalent to the condition that all its interior angles be less than 180°.) More generally, a region in a real vector space is convex if whenever two points x and y are in the region then so is any point tx + (1 - t)y, where t lies in the interval [0, 1]. See the immediately following entries for additional uses of the descriptor “convex.” Cf. concave. convex function   A function is convex if the chord joining any two points of its graph lies entirely above the graph. Cf. concave function. convex set   A subset X of a partially ordered set is convex if for any elements a, b in X such that a b, then all elements x satisfying a x b are also in X. cos   See cosine. cosecant    ARTICLE   A periodic trigonometric function defined on angles, usually abbreviated “csc.” It is the multiplicative inverse of the sine function. See the article for a complete exposition. cosine    ARTICLE   A periodic trigonometric function defined on angles, and usually abbreviated “cos.” See the article for a complete exposition. cot   See cotangent. cotangent    ARTICLE   A periodic trigonometric function defined on angles, usually abbreviated “cot.” It is equal to the multiplicative inverse of the tangent function. See the article for a complete exposition. countable   A set is countable if it is finite, or if it is infinite and bijective to the set of natural numbers (finite ordinals), i.e., if there exists a complete one-to-one mapping of the set in question onto the set N. Sets that are both countable and infinite are sometimes called denumerable. Georg Cantor proved that sets may be uncountably infinite, for example the set of real numbers. Related MiniText: Infinity -- You Can't Get There From Here... countable chain condition   See chain condition. countably infinite   See countable cover   Topology: a collection of sets which contains a given set. If the sets in the covering collection are open sets, the cover is called an open cover. Partially ordered sets: If x and y are elements of a partially ordered set such that x y, and such that there is no z such that x z y, then we say that x covers y. Graph Theory: An edge or vertex of a graph is said to cover (verb) those vertices or edges, respectively, that it is incident on. A set of edges or vertices is said to cover any vertex or edge covered by any element of that set. A set of edges or vertices that covers all the vertices or edges, respectively, of the graph is called a cover (noun), usually with a specification of whether it consists of edges or vertices. See edge cover, vertex cover. cross product   See vector product. csc   See cosecant. cube   A regular polyhedron having six square faces. More generally, an n-dimensional cube in the first quadrant of a Euclidean space with one vertex at the origin is given by the collection of all n-tuples of the form (e1,e2, ... , en), with each ei an element of the set {0,1}. Cf. platonic solid. Related article: Platonic Solids cub set   Closed, unbounded set. See closed set. cycle   Algebra: See permutation. Graph Theory: A graph C whose vertices and edges can be numbered {v1, v2, ..., vn} and {e1, e2, ..., en}, respectively, for some n 1, such that ei is incident on vi and vi + 1 for every i < n, and en is incident on vn and v1. A cycle with n vertices is denoted by Cn. For a given graph G, a cycle of G (or a cycle in G) is a subgraph of G that is also a cycle. Cycles are sometimes also called circuits. D-system   Set Theory: A family A of sets is called a D-system (also called a quasi-disjoint family) if and only if there is a fixed set r, called the root of the D-system, such that for any two elements x and y of A, x y = r. It is a theorem that every uncountable family of finite sets has a sub-family which forms a D-system. Cf. almost disjoint.
		convergent series – D-system

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