Primitive recursive function: Difference between revisions

Revision as of 08:40, 23 June 2024

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| 2=''Successor function'': The 1-ary successor function ''S'', which returns the successor of its argument (see [[Peano postulates]]), that is, <math>S(x) \ \stackrel{\mathrm{def}}{=}\ x + 1</math>, is primitive recursive.

| 3=''Projection functionfunctions'' <math>P_i^k</math>: For all natural numbers <math>i, k</math> such that <math>1\le i\le k</math>, the ''k''-ary function defined by <math>P_i^k(x_1,\ldots,x_k) \ \stackrel{\mathrm{def}}{=}\ x_i</math> is primitive recursive.

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More complex primitive recursive functions can be obtained by applying the [[operation (mathematics)|operation]]s given by these axioms: