 In other words, \(\mu y f(\vec{n},y)\) is equal to the least \(m\) such that \(f(\vec{n},m) = 0\) provided that such an \(m\) exists and also that \(f(\vec{n},i)\) is defined but not equal to 0 for all \(0 \leq i &lt; m\). On the other hand, \(\mu y f(\vec{n},y)\) is undefined just in case either there is no \(m\) such that \(f(\vec{n},m) = 0\) or there is such a \(m\) but \(f(\vec{n},i)\) is undefined for some \(i &lt; m\).