By D. A. Holton, J. Seberry

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E. the relation between consecutive integers. This relation is asymmetrical, but not We can, however, derive from it, transitive or connected. " " mathematical ancestral the method of induction, the by relation which we considered relation will This than or equal to " among in the preceding chapter. be the same as " less For purposes of generating the series of inductive integers. " equal m of n but not comes to the same thing) an ancestor of n in the sense in which identical with n, or (what when the successor of m is a number is its own ancestor.

Between a and b is between x and y, then b between a and y. (6) If x and y are between a and b, then either x and y are identical, or x is between a and y, or x is between y and b. is If b is (7) a: b and y are and #. between a and x and identical, or x is also between a and between and y, y, or y then either is between These seven properties are obviously verified in the case of points on a straight line in ordinary space. Any three-term relation which verifies them gives rise to series, as following definitions.

These words have been already defined, recalled here for the sake of the following definition The field of a domain together. (4) 1 relation consists of its This term is due to but are : domain and converse C. S. Peirce. The Definition of Order One (5) it relation is 33 said to contain or be implied by another if holds whenever the other holds. be seen that an asymmetrical relation It will is the same thing whose square is an aliorelative. It often happens that a relation is an aliorelative without being asymmetrical, though an asymmetrical relation is always an aliorelative.