Probability of $0$ I was watching the following video Stochastic Supertasks (watch from 7:00 to 7:13), and they  said that an event was "... possible 
 but happens zero percent of the time ...". I'm confused with how that works?
I've only ever done an extremely small amount of probability in high school, but I was told that if something has a probability of 0, it's impossible! That is, it can't happen at all (as opposed to it happening, but with unlikely probability). Similarly, I was told that if an event has a probability of 1 then the event WILL happen.
Question: What does it mean for an event to have zero probability? Does that mean it's impossible? If not, why not?
Thanks
 A: The reason is probably that in high school one is concerned with application and then odd situation that can be produced in theoretical mathematics is of little concern. One never have situation where infinite really means infinite.
If we allow for infinities. Take for example you throw a dice infinite number of times, you will get a sequence of numbers. The probability that you get that actual sequence however is zero. 
Another problem is with uniform continuous distributions, the probability that you pick a certain number is zero. Here however applications have the feature that you can't determine the outcome exactly, but you settle for an approximation which means that you in practice doesn't consider the probability of a single outcome, but rather a range of outcomes.
On the other hand in applications we still consider some things with still positive probability to be so improbable that they are considered impossible. We have for example a non-zero probability that all nuclear waste decays into non-radiactive isotopes today. While that would be nice it's simply are not going to happen.
Mathematically one uses the term "almost never" (or similar) for events with probability of $0$ and "almost certainly" (or similar) for events with probability of $1$.
A: 
I've only ever done an extremely small amount of probability in high school, but I was told that if something has a probability of 0, it's impossible! 

You should have been told that if an event is impossible, then it has a probability of zero.   That's not the same thing.
(If it is a duck, then it is a bird; but if it is a bird, then it may or may not be a duck.)
Impossible events do have a probability of zero, but there are also events which, while possible, have zero measure.   (At least, theoretically.)
For example: the lifespans of lightbulbs may be modelled as being continuous random variables with exponential distribution.   So two lightbulbs being independently tested are assigned zero probability of failing at exactly the same time; but it is possible.
(Though, in practice, there is a limit on precision of our time measurements.)
