| __ipedia.com: Primitive recursive function Article__ *(Site not responding. Last check: 2007-10-21)* |

| | The primitive **recursive** **functions** are a strict subset of the **recursive** **functions** (which are exactly those **functions** which we call "computable"; see Church-Turing thesis). |

| | Primitive **recursion**: Given f a k-ary primitive **recursive** **function** and g a (k+2)-ary primitive **recursive** **function**, the (k+1)-ary **function** defined as the primitive **recursion** of f and g, i.e. |

| | Many other familiar **functions** can be shown to be primitive **recursive;** some examples include conditionals, exponentiation, primality testing, and mathematical induction, and the primitive **recursive** **functions** can be extended to operate on other objects such as integers and rational numbers. |

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