Let a be a natural number and let g: \mathbf{N} \times \mathbf{N} \rightarrow \mathbf{N} be a function. The function h: \mathbf{N} \rightarrow \mathbf{N} is said to be defined by primitive recursion from the constant a and the function g if
- h(0) = a,
- h(n+1) = g(n, h(n)).
Example:
- h(0) = 1
- h(n+1) = g(n, h(n)) = (n+1) \times h(n)
is the well-know faculty function.
( Open University, M381 ML-1 )
Beautiful, isn't it?
Indeed - beautiful - I just 'get it', as opposed to the comprehensively verbose Wikipedia article. I used to think I didn't need to do English at school - who needs to 'communicate' when you have maths? Ha!
ReplyDeleteKobath,
ReplyDeleteExactly.