It is easy to see, and not difficult to prove, that the relation " less than ", so defined, is asymmetrical, transitive, and connected, and has the [ natural ] numbers for its field [ i . e . both domain and converse domain are the numbers ] . " ( 1919 : 35)
2.
A relation is connected when, given any two different terms of its field [ both domain and converse domain of a relation e . g . husbands versus wives in the relation of married ] the relation holds between the first and the second or between the second and the first ( not excluding the possibility that both may happen, though both cannot happen if the relation is asymmetrical ) . ( 1919 : 32)
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