Order Relations
Learn about order relations, the usual order, and the dual order.
We'll cover the following
Order relation
A relation
For any
, there is . This means that is reflexive. For any
, if and , then . This means that is antisymmetric. For any
, if and , then . This means that is transitive.
The relation
Note: We will interchangeably use both terms, i.e., order relation and partial order, to become comfortable with using both terms.
For a set
Examples
The subset relation is a partial order for any set of the sets. Let
As every set is a subset of itself, this means that
is a reflexive relation. For any sets
, if and , then . This means that is an antisymmetric relation. For any sets
, if and , then . This means that is a transitive relation.
Get hands-on with 1200+ tech skills courses.