A total order satisfies the conditions for a Partial Order plus the comparability condition. A Relation
is a partial order on a Set if
- 1. Reflexivity: for all
- 2. Antisymmetry: and implies
- 3. Transitivity: and implies ,
and is a total order if, in addition,
- 4. Comparability: For any , either or .
See also Partial Order, Relation
© 1996-9 Eric W. Weisstein
1999-05-26