Primitive recursive function: Difference between revisions

Revision as of 20:48, 21 July 2004

Revision as of 22:31, 2 September 2004

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:(Note: here ''P''₁³ is a function, which takes 3 arguments and returns the first one.)

:Note that ''P''₁¹ is simply the [[identity function]]; its inclusion is required by the definition of the primitive recursion operator above; it plays the role of ''hf''. The composition of ''S'' and ''P''₁³, which is primitive recursive, plays the role of ''g''.

;[[Subtraction]]: We can define ''limited subtraction'', i.e. subtraction that bottoms out at 0 (since we have no concept of negative numbers yet). First we must define the "predecessor" function, which acts as the opposite of the successor function.