On a set , a relation “” is called a Simple Order (sometimes called an Order Relation or Linear Order) if the following hold for all :
- Comparability: either or ;
- Non-Reflexivity: ;
- Transitivity: and .
When dealing with a Simple Order it is more common to use the symbol rather than the symbol for “relates to” because of the added intuition it brings.
Note: Non-Reflexivity can also be thought of as is FALSE for all .