mu operator

In computability theory, the μ-operator is the operator which when applied to a given computable function f is a computable function returning the first value for which f is zero. For a given function

f:\mathbb{N}\rightarrow\mathbb{Z}

\mu y\left f(y)=0\right =z

if and only if

f(z)=0

and

for every

y, f(y) is defined and f(y)>0 .

Using similar definitions, this idea can be extended to a μ-formula for any well-formed formula φ of one free variable, written

\mu y\left \phi(y)\right

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