Primitive recursive function: Difference between revisions

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Up to this section, the true value was associated with 1 and the false value was associated with 0. Then, the truth value of a variable x is undefined, as well as S(x). But the truth value of 0 is defined as false. Therefore, phrasing the sentence in terms of false (or 0) makes the behavior of the If function well defined.
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Undid revision 1250446855 by Pedro A L Barbosa (talk): both descriptions are identical on natural numbers, and this is where these functions are defined on
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= & z & \text{ by Def. } P_2^2 . \\
\end{array}</math>.
That is, <math>\textit{If}(x,y,z)</math> returns the elsethen-part, <math>zy</math>, if the if-part, <math>x</math>, is falsetrue, and the thenelse-part, <math>yz</math>, otherwise.
 
=== Junctors ===