## pre-order

<theory>

1. traversal.

2. A relation R is a pre-order if it is reflexive (x R x) and transitive (x R y R z => x R z). If it is also antisymmetric (x R y R x => x = y) then it is a partial ordering.

<theory>

1. traversal.

2. A relation R is a pre-order if it is reflexive (x R x) and transitive (x R y R z => x R z). If it is also antisymmetric (x R y R x => x = y) then it is a partial ordering.