# Folklore

There exist several traditional methods of construction of the natural entireties but that of the entireties of von Neumann is often looked like simplest.

## Method of von Neuman

On the basis of the Set theory, one identifies 0 with the Empty set, then one builds the successor of a Entier naturalness like the whole of the natural entireties which precede it. More precisely, the natural entireties are built starting from the following rules:

1. the empty set $\ emptyset$ is a natural entirety noted 0.

2. If NR is a natural entirety, the unit NR U {NR} is also a natural entirety, called the immediate successor of NR.
3. Entire naturalness is built starting from rules 1 and 2.

For example, the immediate successor of 0 is: 0 U {0} = {0} = 1

That of 1:1 U {1} = {0} U {1} = {0,1} = 2

That of 2:2 U {2} = {0,1} U {2} = {0,1,2} = 3

The axiom of infinite is necessary to ensure the existence of a unit containing all the natural entireties. The intersection of all the whole of this type (containing 0 and closed for the operation successor) is then the whole of the natural entireties. One can check that this last satisfies the Axiomes of Peano.

## See too

 Random links: Pothin of Lyon | Dipodomys ingens | The Hand off Fate | Akron Goodyear Wingfoots | Modeling and Analysis off Real Time and Embedded systems | Folklore