Definition:Natural Numbers/Zermelo Construction

Theorem
The natural numbers $\N = \left\{{0, 1, 2, 3, \ldots}\right\}$ can be defined as a series of subsets:


 * $0 := \varnothing = \left\{{}\right\}$
 * $1 := \left\{{0}\right\} = \left\{{\varnothing}\right\}$
 * $2 := \left\{{1}\right\} = \left\{{\left\{{\varnothing}\right\}}\right\}$
 * $3 := \left\{{2}\right\} = \left\{{\left\{{\left\{{\varnothing}\right\}}\right\}}\right\}$
 * $\vdots$

However, this approach is rarely seen, as it is less useful that the more prevalent method of construction as Elements of Minimal Infinite Successor Set.

Also see

 * Definition:Natural Numbers for more usual techniques of defining $\N$.