### Some articles on *primitive recursive functions, function, primitive, recursive functions, recursive, functions*:

Primitive Recursive Function - Examples - Subtraction

... Because

... Because

**primitive recursive functions**use natural numbers rather than integers, and the natural numbers are not closed under subtraction, a limited subtraction ... This limited subtraction**function**sub(a,b) returns if this is nonnegative and returns 0 otherwise ... The predecessor**function**acts as the opposite of the successor**function**and is recursively defined by the rules pred(0)=0, pred(n+1)=n ...Primitive Recursive Function

... The

... The

**primitive recursive functions**are defined using**primitive**recursion and composition as central operations and are a strict subset of the total µ-**recursive functions**(µ-**recursive**... In computability theory,**primitive recursive functions**are a class of**functions**that form an important building block on the way to a full formalization ... These**functions**are also important in proof theory ...Algorithm Characterizations - 1943, 1952 Stephen Kleene's Characterization - 1943 "Thesis I", 1952 "Church's Thesis"

... Every effectively calculable

... Every effectively calculable

**function**(effectively decidable predicate) is general**recursive**" (First stated by Kleene in 1943 (reprinted page 274 in Davis, ed ... appears also verbatim in Kleene (1952) p.300) In a nutshell to calculate any**function**the only operations a person needs (technically, formally) are the 6**primitive**operators of "general" recursion (nowadays ... (decision) procedure or algorithm, for the case of a**function**(predicate) of natural numbers" (p ...μ-recursive Function - Definition

... The μ-

... The μ-

**recursive functions**(or partial μ-**recursive functions**) are partial**functions**that take finite tuples of natural numbers and return a single natural number ... They are the smallest class of partial**functions**that includes the initial**functions**and is closed under composition,**primitive**recursion, and the μ operator ... The smallest class of**functions**including the initial**functions**and closed under composition and**primitive**recursion (i.e ...Grzegorczyk Hierarchy - Relation To

... The definition of is the same as that of the

**Primitive Recursive Functions**... The definition of is the same as that of the

**primitive recursive functions**, RP, except that recursion is limited ( for some j in ) and the**functions**are explicitly included in ... Thus the Grzegorczyk hierarchy can be seen as a way to limit the power of**primitive**recursion to different levels ... It is clear from this fact that all**functions**in any level of the Grzegorczyk hierarchy are**primitive recursive functions**(i.e ...### Famous quotes containing the words functions and/or primitive:

“Empirical science is apt to cloud the sight, and, by the very knowledge of *functions* and processes, to bereave the student of the manly contemplation of the whole.”

—Ralph Waldo Emerson (1803–1882)

“The glory of the farmer is that, in the division of labors, it is his part to create. All trade rests at last on his *primitive* activity.”

—Ralph Waldo Emerson (1803–1882)

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