ABSTRACT
I.1 The system of natural numbers, as ordered by the predicate1 ‘mn.m is less than n’, has the following properties (amongst others):
—the ordering is transitive: for any natural numbers k, l, m, if k is less than l, and l than m, then k is less than m;
—the ordering is connected: for any natural numbers m, n, either m is less than n, or m is the same as n, or n is less than m;
—the ordering is irreflexive: no natural number is less than itself; —there is a least natural number-that is, a natural number than which
none is less; —every natural number has a successor: for every natural number m,
there is a natural number n such that m is less than n but there is no natural number between m and n.
