User blog:Testitemqlstudop/On mapping positive integers to ordinals

Recently, I have made a pathetic system to map all positive integers to ordinals under e0 one-to-one: Rule 1: map(0) = 0 Rule 2: map(n+2^m-1) = ord(n)+m Unambiguity: This is ony applied for the maximum possible m. Furthermore, it is only applied when (2^m-1)&(n+2^m-1) = 2^m-1, where & is the bitwise AND operator. Rule 3: map(2^n*m) = (w^map(n))map(m) Unambiguity: This is only applied for the maximum possible n. Two questions:

1 - Is it well-defined?

2 - How do I extend it to map higher ordinals?