Mitchell Porter: There is a nonzero probability of death per unit time, and so the probability of literal immortality is infinitesimal, being a product of infinitely many quantities less than 1.

This is mathematically incorrect. If the quantities tend to 1 fast enough, their product will converge to a positive number. For example, if you have a 1/2 chance of living another 50 years, then if you do, a 3/4 chance of another 50, then a 7/8 chance of another 50, and so on, the probability that you will never die is about 0.29.

So the trick is to always be getting better fast enough at not dying.