For all practical purposes if an event has a probability of 0 it cannot occur, but technically, if the sample space is infinite, events with probability 0 are not impossible. For example, we throw a dart at a wall. Although the wall has finite size, it contains infinitely many points, because each point on the wall has 0 size. Therefore, the probability of each individual point is 0, yet if the dart hits the wall, the exact center of the dart must hit some point on the wall. Thus an event with probability 0 must occur.
I was writing a response to
caveman1917's post when I read yours here and… aha!
Now it makes more sense! No offense intended toward
caveman1917's efforts which I appreciate.
It sounds, then, to me like the various Zeno's paradoxes; Achilles and the hare, for example. Theoretically, Achilles can never reach the hare (following the cited example) just as theoretically, in an infinite universe and infinite time, theoretically there will always be a chance for a zero-probabiility thing to happen. Is that correct?
I've been looking at it from the perspective of your first statement — "for all practical purposes." Same with Achilles. In reality, he will reach the hare because we cannot slice time up into infinite, discrete units that the thought experiment requires.
This is where the concept of "infinity" makes 'common sense' kind of out the window, I guess.
Is that then what
caveman1917 was trying to demonstrate with the existence of Ewoks earlier in the thread? I tried following it and my only counter to it, lame as it is, is that a mathematical proof of the existence of Ewoks isn't the same thing as them actually existing. Here, now, in this universe, which is what I understood that
Argumemnon is saying.
Are my perceptions accurate enough?
Applying this to
Jabba's… well… ideas. How have people been mistaken in refuting his "mathematics"?