Pp. 83-106 (24)
The theory of ordinal numbers is a natural and very powerful generalization
of the order-theoretical properties of natural numbers. In particular it furnishes
transfinite induction, a method for constructing rather complicated mathematical
concepts and for proving properties valid beyond the natural numbers. Ordinal
numbers can also serve as a basis for introducing cardinal numbers. The
latter evaluate “how many elements” a set possesses, being thus a kind of “quantitative”
generalization of natural numbers, widely used in mathematics.