connected subset but if the loss is finite then any sequence generated by the iteration equation three converges to some fixed point so you know basically saying that here we oh this is not the loss i'm sorry um no this is the domain never mind i'm an idiot this is basically saying that this algorithm will converge okay and they define here what it means for a pattern to be stored and retrieved and that's for establishing what the kind of storage capacity of a hopfield network is so we've established that the update