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Recursive predicate

From Encyclopedia of Mathematics
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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=49395
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article