Also, we are concerned about the "uninterrupted continuance" of that information embodied as our "sense of self". And these two aspects, (our information store and our awareness of it), cannot be totally divorced from one another, vis. if our "soul" goes on but not our memories, what sort of satisfaction can be gotten here?
There is another hypothetical form of death which even if proven to be not possible is nevertheless instructive. Suppose that aging and disease are both eliminated. What happens to us in the extremely long run? What if we actually did live on forever (or its reasonable facsimile)?
Since the physical brain structure will not carry an infinite amount of information, those memories of little value (those not constantly reinforced) must be lost. So we find that instead of death as a sharp discontinuity we trade it in for death as a long drawn out process of gradual replacement. And in the long run we can no longer seriously call ourselves the same person. We represent, rather, the "continuity" of a specific individual as an "information node" where memories are temporarily stored in a logical manner with respect to the external physical and social world.