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:

    The manifestation of poetry in external life is formal perfection. True sentiment grows within, and art must represent internal phenomena externally.
    Franz Grillparzer (1791–1872)

    The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.
    Pamela Patrick Novotny (20th century)