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G-2 Glossary in Java Drawer QR in Java G-2 Glossary

G-2 Glossary generate, create qr none with java projects Basice Knowlege of iReport pairs (a, b), where tomcat QR Code ISO/IEC18004 a E A and b E B. For example, J1, 2} x {x) = {(l, x), (2, x)}. p.

48 ceiling The ceiling of a real number x, denoted rxJ, is the least integer greater than or equal to x. For example, [3 -4, rO[= 0 and F-341 = -3. p.

76 chain A chain is a trail in a directed network, that is, a walk in which the arcs are distinct and can be followed in either direction. p. 448 chromatic number The chromaticnumber of a graph is the smallest natural number n for which an n-coloring exists.

p. 423 circuit A circuit in a pseudograph is a closed trail. p.

303 coloring A coloring of a graph is an assignment of colors to vertices so that adjacent vertices have different colors. An n-coloring is a coloring which uses n colors. p.

423 combination A combination of objects is a subset of them. An r-combination is a subset of r objects. For example, {Charles, Andrew) is a 2-combination of the members of the British royal family.

p. 218. common difference See the definition of arithmetic sequence.

common ratio See the definition of geometric sequence. comparable Two elements a and b are comparable with respect to a partial order -< if and only if either a -< b or b -< a. For example, with respect to "divides" on N, 2 and 6 are comparable, but 2 and 7 are not.

p. 64 complement The complement of a set A, written AC, is the set of elements which belong to some universal set, defined by the context, but which do not belong to A. For example, if the universal set is R, then {x I x < I}c = composition The composition of functions f: A -- B and g: B-* C is the function g o : AC defined by g o f (a) = g(f(a)) for a c A.

For example, if f and g are the functions R - R defined by f (x) = x + 2 and g(x) = 2x -3, then g o f (x) = 2x + l. p. 82.

conclusion See argument. {xlx>l}. p.445 complete bipartite The complete bipartite graph on two sets VI and V2 is th QR for Java at bipartite graph whose vertices are the union of VI and V2 and whose edges consist of all possible edges between these sets. p. 288.

complete graph The c omplete graph on n vertices is that graph which has n vertices, each pair of which are adjacent. p. 288 complexity The complexity of an algorithm is a function which gives an upper bound for the number of operations required to carry out the algorithm.

It is usually specified in general terms, by giving another function of which it is Big Oh. The binary search algorithm, for example, has component A component of a graph is a connected subgraph which is properly contained in no connected subgraph with a larger vertex set or larger edge set. p.

310 composite A composite number is a natural number larger than I which is not prime; for example, 6 and 10. p. 114.

complexity (9(10g 2 n). p. 246 congruence class The congruence class of an integer a (mod n) is the set {b E Z I a b (mod n)] of all integers to which a is congruent mod n; for example, the congruence class of 5 (mod 7) is the set 7Z + 5 of integers of the form 7k + 5. p. 126 congruence mod n Integers a and b are congruent module n, where n > I is a natural number-and we write a - b (mod n)-if a -b is divisible by n.

For example, -2 -1 I0 (mod 4), but 7 # -19 (mod 12). p. 126 connected A pseudograph is connected if there is a walk between any two vertices.

p. 305 contradiction A contradiction is a compound statement that is always false. For example, ((-p) A q) A (p V (-q)) is a contradiction.

(Examine the truth table.) p. 20 contrapositive The contrapositive of the implication "p q" is the implication "(-q) -* (-p).

" For example, the contrapositive of "If a graph is planar, then it can be colored with at most four colors" is "If a graph cannot be colored with at most four colors, then it is not planar." p. 5 converse The converse of the implication p -* q is the implication q -- p.

For example, the converse of "If a graph is planar, then it can be colored with at most four colors" is "If a graph can be colored with at most four colors, then it is planar." p. 4 countable A set is countable if and only if it is finite or countably infinite.

For example, the rational numbers and the set of natural numbers not exceeding 1000 are both countable sets. p. 90 countably infinite A countably infinite set is an infinite set which has the cardinality of the natural numbers.

For example, the rational numbers form a countably infinite set. p. 90 cut An (s, t)-cut in a directed network with vertex set V, two of whose members are s and t, is a pair of disjoint sets S and T, s E S, t e T.

whose union is V. p. 444 cycle A cycle in a pseudograph is a circuit in which the first vertex appears exactly twice (at the beginning and the end) and in which no other vertex appears more than once.

An n-cycle is a cycle with n vertices. p. 303.

D degree The degree j2ee QR of a vertex in a pseudograph is the number of edges incident with that vertex. p. 286.

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