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Difference between revisions of "Recursive predicate"

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A [[Predicate|predicate]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080300/r0803001.png" /> defined on the natural numbers, such that the function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080300/r0803002.png" /> defined on the natural numbers by the condition
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A [[Predicate|predicate]]  $  P( x _ {1} \dots x _ {n} ) $
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defined on the natural numbers, such that the function  $  f $
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defined on the natural numbers by the condition
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$$
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f( x _ {1} \dots x _ {n} )  = \left \{
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\begin{array}{ll}
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1  & \textrm{ if }  P( x _ {1} \dots x _ {n} )  \textrm{ is  true  },  \\
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0 & \textrm{ if }  P( x _ {1} \dots x _ {n} )  \textrm{ is  false  } ,  \\
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\end{array}
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\right .$$
  
 
is a [[Recursive function|recursive function]].
 
is a [[Recursive function|recursive function]].

Latest revision as of 14:55, 7 June 2020


A predicate $ P( x _ {1} \dots x _ {n} ) $ defined on the natural numbers, such that the function $ f $ defined on the natural numbers by the condition

$$ f( x _ {1} \dots x _ {n} ) = \left \{ \begin{array}{ll} 1 & \textrm{ if } P( x _ {1} \dots x _ {n} ) \textrm{ is true }, \\ 0 & \textrm{ if } P( x _ {1} \dots x _ {n} ) \textrm{ is false } , \\ \end{array} \right .$$

is a recursive function.

How to Cite This Entry:
Recursive predicate. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Recursive_predicate&oldid=13803
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article