Recall the relation successor := hx, x + 1i : x ∈ Z≥0 . Prove by induction on k that, for any integer x and any positive integer k, we have that hx, x + ki is in the transitive closure of successor....

Recall the relation successor := hx, x + 1i : x ∈ Z≥0 . Prove by induction on k that, for any integer x and any positive integer k, we have that hx, x + ki is in the transitive closure of successor. (In other words, you’re showing that the transitive closure of successor is ≥. Note that you cannot rely on the algorithm in Figure 8.25 because Z≥0 is not finite!)