**Description: **Define the class of
natural numbers, which are all ordinal numbers that
are less than every limit ordinal, i.e. all finite ordinals. Our
definition is a variant of the Definition of N of [BellMachover]
p. 471. See dfom2 4801 for an alternate definition. Later, when we
assume
the Axiom of Infinity, we show is a set in omex 7545, and
can then be defined per dfom3 7549 (the smallest inductive set) and
dfom4 7551.
*Note*: the natural numbers are a subset of the ordinal numbers
df-on 4540. They are completely different from the
natural numbers
(df-nn 9947) that are a subset of the complex numbers
defined much later
in our development, although the two sets have analogous properties and
operations defined on them. (Contributed by NM,
15-May-1994.) |