Order theory

Order theory is a field of mathematics. It concerns itself with being able to compare different elements of a set. Given a binary relation it is then possible to put all the elements of the set in a certain order. It is also possible to say that a certain element "comes before" another one, for that relation. Another way to say this is to say that one of the two is "smaller than" the other.

For a specific set to be ordered it must be:

reflexive: each element of the set is within a relation with itself.

anti-symmetric: if A and B are in relation, and B is also in a relation with A, then A must be equal to B.

transitive: if A and B in a relation, and B is in a relation with C, then A and C must be in a relation.