## total function

A function which is defined for all arguments of the appropriate type. The opposite is a partial function.

Last updated: 1997-01-10

## totally ordered

Having a total ordering.

Last updated: 1997-01-10

## totally ordered set

A set with a total ordering.

## total ordering

A relation R on a set A which is a partial ordering; i.e. it is reflexive (xRx), transitive (xRyRz => xRz) and antisymmetric (xRyRx => x=y) and for any two elements x and y in A, either x R y or y R x.

See also equivalence relation, well-ordered.

Last updated: 1995-02-16

### Nearby terms:

Toshiba Corporation ♦ TOSS ♦ **total function** ♦ totally ordered ♦ totally ordered set

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