The notation for a preorder, namely (X, ≤), refers to two pieces of structure: a set called X and a relation called ≤ that is reflexive and transitive. We want to add to the concept of preorders a wa...The notation for a preorder, namely (X, ≤), refers to two pieces of structure: a set called X and a relation called ≤ that is reflexive and transitive. We want to add to the concept of preorders a way of combining elements in X, an operation taking two elements and adding or multiplying them together. However, the operation does not have to literally be addition or multiplication; it only needs to satisfy some of the properties one expects from them.
