Yesterday’s Dinosaur Comics comic claims that if you live forever yet have an infinite natural life span but can still die from, say, falling down the stairs, you are guaranteed to die because in an infinite lifespan you have an infinity of opportunities to fall down the stairs so at some point you will eventually do so. Suppose this occurs at time t. Then there is a finite amount of time between your birth and time t, so only a finite number of events can happen in your life because events take up time and there is only so much of that available.

Now take any event, e, that does not result in your death. We can safely say that there are infinitely many such events so we can’t run out of them: if not, then if you happened to fall down the stairs at time t + 1 you would potentially have nothing to do for that extra slot of time because you’d used up all the events. Keep re-choosing e until e does not occur before time $t$—but then the event can never happen because you’re dead. Contradiction, so this whole method of reasoning doesn’t work, so there is no guarantee that you fall down the stairs.

This is why I hate infinity, so why I hate analysis. How the heck am I going to survive set theory where you have “bigger” infinities?