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## Thursday, March 17, 2011

### Primitive recursion

I really appreciate the books on Mathematical Logic from M381. Take for example the very concise definition of primitive recursion.

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?

1. 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!

2. Kobath,

Exactly.

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)