 A series (linear ordering) is defined as a relation that is irreflexive \(\forall x (\lnot x\relR x)\), transitive \(\forall x \forall y \forall z (x\relR y \amp y\relR z \supset x\relR z)\), and connected \(\forall x \forall y (x\relR y \lor y\relR x)\). (∗204·01) (These properties are restricted to a specific domain for each relation. Thus a connected relation will hold between any two members of a given domain.) This is now called a linear ordering of a given set.