$13.$ Suppose that $\backslash ($ L $\backslash )$ is such that there exists a Turing machine that enumerates the elements of $\backslash ($ L $\backslash )$ in proper order. Show that this means that $\backslash ($ L $\backslash )$ is recursive. $4.$ In the general halting problem, we ask for an algorithm that gives the correct answer for any $\backslash ($ M $\backslash )$ and $\backslash ($ w $\backslash ).$ We can relax this generality, for example, by looking for an algorithm that works for all $\backslash ($ M $\backslash )$ but only a single $\backslash ($ w $\backslash ).$ We say that such a problem is decidable if for every $\backslash ($ w $\backslash )$ there exists a $($possibly different$)$ algorithm that determines whether or not $\backslash (($M$,$ w$)\backslash )$ halts. Show that even in this restricted setting the problem is undecidable.