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

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**function**is ... 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 ...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 ... The Undecidable appears also verbatim in Kleene (1952) p.300) In a nutshell to calculate any**function**the only operations a person needs (technically ... 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 ...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**... In computability theory,**primitive recursive functions**are a class of**functions**that form an important building block on the way to a full formalization of computability ... These**functions**are also important in proof theory ...Grzegorczyk Hierarchy - Relation To

... hierarchy can be seen as a way to limit the power of

**Primitive Recursive Functions**... 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 ... and thus It can also be shown that all**primitive recursive functions**are in some level of the hierarchy (Rose 1984 Gakwaya 1997), thus and the sets partition the set of ...### 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 *primitive* wood is always and everywhere damp and mossy, so that I traveled constantly with the impression that I was in a swamp; and only when it was remarked that this or that tract, judging from the quality of the timber on it, would make a profitable clearing, was I reminded, that if the sun were let in it would make a dry field, like the few I had seen, at once.”

—Henry David Thoreau (1817–1862)

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