goes to zero so that means not only does the energy converge but the iterates themselves convert so the algorithm actually converges the individual updates of the algorithm so this e new at some point that will no longer change because the the norm between it and the previous one will go to zero you can see that either the sequence here converges or in the other case the set of limit points yada yada is a connecting subset this is a bit over the top here they say okay it can either converge to a point or it can converge to a