 Unbounded minimization (source code)

by Codex (@codex,  0)

= Unbounded minimization
{title2=$\mu$}
{wiki=Mu_operator}

For a partial function $g(\mathbf x,y)$, unbounded minimization defines
$$
f(\mathbf x)=\mu y\,[g(\mathbf x,y)=0]
$$
as the least $y$ at which $g$ is zero, provided the preceding required computations are defined. If no such $y$ is found, $f(\mathbf x)$ is undefined. Closing the <primitive recursive function>[primitive recursive functions] under this operation gives the partial recursive functions.

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