Definition:Natural Numbers/Von Neumann Construction

Definition
Let $\omega$ denote the minimally inductive set.

The natural numbers can be defined as the elements of $\omega$.

Following Definition 2 of $\omega$, this amounts to defining the natural numbers as the finite ordinals.

In terms of the empty set $\O$ and successor sets, we thus define:

This can be expressed in detail as:

Also see

 * Definition:Minimally Inductive Set


 * Minimally Inductive Set forms Peano Structure