In terms of Ray Bradbury's Fahrenheit 451, the concept of immortality can only apply to books—and not the books themselves, as the burning of books shows that they, like human life, can only withstand so much; but it is the information that is contained in books that is immortal as long as it is remembered.
When Montag has killed Beatty, and destroyed the Mechanical Hound, he makes it to the river, where he changes his clothes to those that Faber gave him, leaving his own scent behind in case he is pursued by another hound. Then he drifts down the river. Soon he finds others like himself, others who value books, who watch with him as society is destroyed by bombs, and who move forward to join still others who wish to save books, rebuild society, and remember what history has taught them, what people wrote about over the years, even if they don't hold the actual books in their hands. It is in this that the inference to "immortality" is made. Granger sums it up when he refers to the mythical phoenix, burned and reborn from the ashes of the fire. (The bird is symbolic of hope.) He relates that the bird would build a pyre (a pile of sticks or other combustibles) and burn himself. Then he "sprang out of the ashes," reborn. This would occur every "few hundred years." Granger draws a comparison of the bird to what mankind seems to do, however, Granger draws a distinct line between what the mythical phoenix did and what mankind does—mankind has knowledge, understanding:
We know the damn silly thing we just did. We know all the damn silly things we've done for a thousand years and as long as we know that and always have it around where we can see it, someday we'll stop making the goddamn funeral pyres and jumping in the middle of them. We pick up a few more people that remember every generation.
And so, it is the memory of the past, a past recorded in so many books (now gone), that Granger believes will one day save humanity. That while individuals may not live forever, the future generations will benefit as long as there are those who remember: these people carry on the knowledge Granger believes mankind needs to survive, in order to stop making the same mistakes over and over again.