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?

I think it means more the sense “if you roll a dice and keep rolling forever, the chance that you will roll a 6 is 1”- it’s “almost surely”. (See also: http://en.wikipedia.org/wiki/Almost_everywhere)