A final dissolution

I am reading John Banville's novel, The Sea, and came across a passage about the impossibility of immortality:

We carry the dead with us only until we die too, and then it is we who are borne along for a little while, and then our bearers in their turn drop, and so on into the unimaginable generations. I remember Anna, our daughter Claire will remember Anna and remember me, then Claire will be gone and there will be those who remember her but not us, and that will be our final dissolution. True, there will be something of us that will remain, a fading photograph, a lock of hair, a few fingerprints, a sprinkling of atoms in the air of the room where we breathed our last, yet none of this will be us, what we are and were, but only the dust of the dead.

The wife of the narrator in this book is Anna, dead of cancer. I don't know whether or not the author had a similar experience. Probably. The older one gets, the more one is bound to think about mortality; Banville is five years older than I am.