Template:PartialTotalOrdering

It is not demanded of, defined in its most general form on a set $S$, that every pair of elements of $S$ is related by. They may be, or they may not be, depending on the specific nature of both $S$ and.

If it is the case that is a connected relation, that is, that every pair of distinct elements is related by, then  is called a.

If it is not the case that is connected, then  is called a.

Beware that some sources use the word partial for which may or may not be connected, while others insist on reserving the word partial for one which is specifically not connected.

It is wise to be certain of what is meant.

As a consequence, on we resolve any ambiguity by reserving the terms for the objects in question as follows:


 * : whose nature ( or ) is not specified


 * : which is specifically not


 * : which is specifically not.