Total relation
Appearance
In mathematics, a binary relation R ⊆ A×B is total (or left total) if the source set A equals the domain {x : there is a y with xRy }. Conversely, R is called right total if B equals the range {y : the is an x with xRy }.
When f: A → B is a function, the domain of f is all of A, hence f is a total relation. On the other hand, if f is a partial function, then the domain may be a proper subset of A, in which case f is not a total relation.
"A binary relation is said to be total with respect to a universe of discourse just in case everything in that universe of discourse stands in that relation to something else."[1]
References
- Gunther Schmidt & Michael Winter (2018) Relational Topology
- C. Brink, W. Kahl, and G. Schmidt (1997) Relational Methods in Computer Science, Advances in Computer Science, page 5, ISBN 3-211-82971-7