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.