Natural Number - Formal Definitions

Formal Definitions

Historically, the precise mathematical definition of the natural numbers developed with some difficulty. The Peano axioms state conditions that any successful definition must satisfy. Certain constructions show that, given set theory, models of the Peano postulates must exist.

Read more about this topic:  Natural Number

Famous quotes containing the words formal and/or definitions:

    That anger can be expressed through words and non-destructive activities; that promises are intended to be kept; that cleanliness and good eating habits are aspects of self-esteem; that compassion is an attribute to be prized—all these lessons are ones children can learn far more readily through the living example of their parents than they ever can through formal instruction.
    Fred Rogers (20th century)

    Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?
    There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.
    Edmond De Goncourt (1822–1896)