Special Types of Binary Relations
Some important types of binary relations R between X and Y are listed below.
Uniqueness properties:
- injective (also called left-unique): for all x and z in X and y in Y it holds that if xRy and zRy then x = z.
- functional (also called right-unique or right-definite): for all x in X, and y and z in Y it holds that if xRy and xRz then y = z; such a binary relation is called a partial function.
- one-to-one (also written 1-to-1): injective and functional.
Totality properties:
- left-total: for all x in X there exists a y in Y such that xRy (this property, although sometimes also referred to as total, is different from the definition of total in the next section).
- surjective (also called right-total): for all y in Y there exists an x in X such that xRy.
Uniqueness and totality properties:
- A function: a relation that is functional and left-total.
- A bijection: a one-to-one correspondence; such a relation is a function and is said to be bijective.
Read more about this topic: Binary Relation
Famous quotes containing the words special, types and/or relations:
“An indirect quotation we can usually expect to rate only as better or worse, more or less faithful, and we cannot even hope for a strict standard of more and less; what is involved is evaluation, relative to special purposes, of an essentially dramatic act.”
—Willard Van Orman Quine (b. 1908)
“The wider the range of possibilities we offer children, the more intense will be their motivations and the richer their experiences. We must widen the range of topics and goals, the types of situations we offer and their degree of structure, the kinds and combinations of resources and materials, and the possible interactions with things, peers, and adults.”
—Loris Malaguzzi (19201994)
“Think of the many different relations of form and content. E.g., the many pairs of trousers and whats in them.”
—Mason Cooley (b. 1927)