=== Converting predicates to numeric functions ===
In some settings it is natural to consider primitive recursive functions that take as inputs tuples that mix numbers with [[truth value]]s (that is ''<math>t''</math> for true and ''<math>f''</math> for false), or that produce truth values as outputs.<ref>Kleene [1952 pp. 226–227]</ref> This can be accomplished by identifying the truth values with numbers in any fixed manner. For example, it is common to identify the truth value ''<math>t''</math> with the number 1 and the truth value ''<math>f''</math> with the number <math>0. Once this identification has been made, the [[indicator function|characteristic function]] of a set ''<math>A''</math>, which always returns 1 or 0, can be viewed as a predicate that tells whether a number is in the set ''<math>A''</math>. Such an identification of predicates with numeric functions will be assumed for the remainder of this article.
