ABSTRACT
In order to develop mathematics within the framework of the axiomatic set theory, it is necessary to define natural numbers. We all know natural numbers intuitively: 0, 1, 2, 3, .. . ,17 , .. . , 324, etc., and we can easily give examples of sets having zero, one, two, or three elements:
Ø has 0 elements.
{Ø} or, in general, {a} for any a, has one element.
{Ø, {Ø}}, or {{{Ø}},{{{Ø}}}}, or, in general, {α,ο} where a ≠ b, has two elements, etc.
