Full Idea
A set is called a 'relation' if every element of it is an ordered pair.
Gist of Idea
A relation is a set consisting entirely of ordered pairs
Source
Michael Potter (Set Theory and Its Philosophy [2004], 04.7)
Book Reference
Potter,Michael: 'Set Theory and Its Philosophy' [OUP 2004], p.65
A Reaction
This is the modern extensional view of relations. For 'to the left of', you just list all the things that are to the left, with the things they are to the left of. But just listing the ordered pairs won't necessarily reveal how they are related.