Solution
= Solution
Fix $x_0\in X$. The property defining $\mathbf{Inf}_X$ depends only on the partial <function> computed, so it is an index set. It is nontrivial: an index of the nowhere-defined <function> is outside it, whereas an index of the total <constant function> $n\mapsto x_0$ has infinite domain and range $\{x_0\}\subseteq X$, and hence lies in it. The <Rice theorem> now shows that this <infinite-domain range-restriction index set> is not computable.