Recursive vs Iterative

[czardas]

Correct. There are well-know functions (mostly useless by themselves) which have been proven not primitive recursive: Ackerman, Sudan, ...

In practice, these academic constructions are only of interest in the theory of computability and such.

This I find hard to imagine, but it is definately most interesting. As is often the case, you open my eyes when you make statements like this. Thanks!