There will always be some probability of dying in a given year. Let's say our futuristic society has solved aging/senescence, and is able to reduce the rate of

There will always be some probability of dying in a given year. Let's say our futuristic society has solved aging/senescence, and is able to reduce the rate of "random death" by about 1% per year, through technology, medicine, brain-redundancy, whatever. So if you have a 1 in 1,000 chance of randomly dying this year, next year it will be about 1 in 1,010. The area under an infinite exponential decay curve is finite. In the scenario above, you have a finite probability of dying, ever. And it's not 100%, either. It could even be quite low. With the numbers above, it's about 10% chance to die, and 90% chance to never die. I know that's counter-intuitive, and it may be that maintaining 1% reduction in random death every year is impossible, but it's not a foregone conclusion that everyone must die. Of course the heat death of the universe presents a problem. That's a good problem to have.