I am reading this book. In the chapter "The Ontology of Metaphysical Realism" the author says:
Many relations are such that pairs of objects enter into them only when taken in a certain order. Thus, being the father of is an asymmetrical relation: if one thing, a , is the father of another thing, b , then b is not the father of a . As logicians put it, it is the ordered pair, <a,b> ( a and b taken in just that order), that exhibits the relation. The three relations we have considered are all two-place or dyadic relations; but obviously there can be three-place, four-place, and, generally, n -place relations.
I understand the idea of an ordered pair when we talk about different objects a and b. However, we do not require that a and b be different. That is, we can write (a, a) and order a and a. What does this mean? How can an object be ordered with itself? On the Internet, I found only a formal definition of an ordered pair, and this did not help me because these definitions are simply expressions for which the characteristic property holds.
Can you explain what (a, a) is with clear examples?