direction

n 1: a line leading to a place or point: "he looked the other

direction"; "didn't know the way home" [syn: {way}]

2: the spatial relation between something and the course along

which it points or moves; "he checked the direction and

velocity of the wind"

3: a general course along which something has a tendency to

develop; "I couldn't follow the direction of his

thoughts"; "his ideals determined the direction of his

career"; "they proposed a new direction for the firm"

4: direction or advice as to a decision or course of action

[syn: {guidance}, {counsel}, {counseling}]

5: the act of managing something; "he was given overall

management of the program"; "is the direction of the

economy a function of government?" [syn: {management}, {managing}]

6: a message describing how something is to be done; "he gave

directions faster than she could follow them" [syn: {instruction}]

7: the act of setting and holding a course; "a new council was

installed under the direction of the king" [syn: {steering},

{guidance}]

8: a formal statement of a command or injunction to do

something; "the judge's charge to the jury" [syn: {commission},

{charge}]

bijection

A {function} is bijective or a bijection or a

one-to-one correspondence if it is both {injective} (no two

values map to the same value) and {surjective} (for every

element of the {codomain} there is some element of the

{domain} which maps to it). I.e. there is exactly one element

of the domain which maps to each element of the codomain.

Only bijective functions have inverses f' where f(f'(x)) ◦

f'(f(x)) ◦ x.

See also {injection}, {surjection}, {isomorphism}.

(1999-08-29)