## 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

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## totally ordered

Having a total ordering.

Last updated: 1997-01-10

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total function ♦ **totally ordered** ♦ totally ordered set ♦ total ordering

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## totally ordered set

A set with a total ordering.

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## 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

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