ABSTRACT
The first objects that we encounter in mathematics are ordered; that is, given (for instance) two different integers, we know that one of them must be larger than the other. Later in mathematics, we find objects that are not ordered in the same way; for instance, there are two different groups of order four, and it makes no sense to say that one of them is “bigger than” or “comes before” the other. Between these two extremes, there are collections for which it is possible to make a sensible statement that some members of the collection are bigger or smaller than others, but for other pairs of members, no comparison is possible. Such a collection of objects, together with the appropriate definition of “bigger than,” is called a partially ordered set, or poset for short.
