Is an empty set a partial order?
Is an empty set a partial order? So by definition, ⊆ is a partial ordering. Now suppose S=∅. Then P(S)={∅} and, by Empty Set is Subset of All Sets, ∅⊆∅. Hence, trivially, ⊆ is a total ordering on P(S). What is meant by partial order set? A partial order defines a notion of comparison. Two elements x and y may stand in any of four mutually exclusive relationships to each other: either x < y, or x = y, or x > y, or x and y are incomparable. A set with a partial order is called a partially ordered...