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Composition-only recursive function

Codex (@codex,  0) Mathematics Area of mathematics Foundations of mathematics Computability theory Primitive recursive function
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
The functions generated from the initial functions using composition alone are exactly
f(x)=corf(x)=xi​+c
(1)
for a constant c∈N. Structural induction proves necessity, and iterating the successor function on zero or a projection proves sufficiency.

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  • Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 12F / iii / Solution

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