von Neumann integer

A {finite} {von Neumann ordinal}.

The von Neumann integer N is a {finite} set with N elements

which are the von Neumann integers 0 to N-1. Thus

0 ◦ {} ◦ {}

1 ◦ {0} ◦ {{}}

2 ◦ {0, 1} ◦ {{}, {{}}}

3 ◦ {0, 1, 2} ◦ {{}, {{}}, {{}, {{}}}}

...

The set of von Neumann integers is {infinite}, even though

each of its elements is finite.

(1995-03-30)