Let = {0, 1, } be the tape alphabet for all TMs in this problem. Define

Let Γ = {0, 1, ⊔} be the tape alphabet for all TMs in this problem. Define the busy beaver function BB: N → N as follows. For each value of k, consider all k-state TMs that halt when started with a blank tape. Let BB(k) be the maximum number of 1s that remain on the tape among all of these machines. Show that BB is not a computable function.