Definition:Strictly Totally Ordered Set

Definition
A strictly totally ordered set is a relational structure $\struct {S, \prec}$ such that the relation $\prec$ is a strict total ordering.

Also known as
It is common to see the term linearly ordered set being used, but some sources use this to refer to a totally ordered set.

As a consequence, on it has been decided that the more cumbersome, but completely descriptive, term strictly totally ordered set be used exclusively.

Also see

 * Definition:Ordered Set
 * Definition:Partially Ordered Set
 * Definition:Totally Ordered Set
 * Definition:Well-Ordered Set


 * Definition:Strictly Ordered Set
 * Definition:Strictly Partially Ordered Set
 * Definition:Strictly Well-Ordered Set