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Zero probability and impossibility

I was recently told "...there is likely a non-zero probability for the combined occurrence of an author writing a story in one universe, the realization of that story in a separate universe, and possibly wormhole connection between these two universes".

Using this example, does non-zero probability imply something is impossible or possible?

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marked as duplicate by Marvis, William, Asaf Karagila, Henning Makholm, t.b. Jun 27 '12 at 22:26

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I have no idea what you are asking. –  copper.hat Jun 27 '12 at 1:42
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What do you mean by "combined"? –  Qiaochu Yuan Jun 27 '12 at 1:46
    
I have the impression he might be asking the following: Let $(A_{i})_{i \in I}$ be a collection of events such that $P(A_{i}) = 0$ for every $i \in I$. Is it possible for $P(\cup_{i \in I}{A_{i}}) \neq 0$? In case it is possible, how do you explain the "paradox" that it is "impossible" for each $A_{i}$ to occur individually but it is possible for at least one of them to occur? (Is that so, Nicholas?) –  madprob Jun 27 '12 at 1:51
    
I can't parse (gramatically) the question. –  leonbloy Jun 27 '12 at 3:04

1 Answer 1

up vote 1 down vote accepted

An event that has zero probability may be possible or impossible.

However, if an event has a nonzero probability, it must be possible; that is, it cannot be impossible.

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How likely would you say, if you believe it must be possible if it is non-zero probability please Eric Stucky? –  Nicholas Jun 27 '12 at 3:16
    
I don't know a good answer to that question. Intuitively, we might guess that there are many more possible events with nonzero probability than zero probability, but I'm not sure if that is actually true. Given that there is no set of all sets, I'm not even sure if it is possible to answer the question. –  Eric Stucky Jun 27 '12 at 3:19
    
But you believe Eric that it is possible for there to be combined occurrence of an author writing a story in one universe, the realization of that story in a separate universe, and possibly wormhole connection between these two universes if it is non-zero probability? Thanks mate. –  Nicholas Jun 27 '12 at 3:23
    
To be honest, I do not know quantum at even such an elementary level to tell you that. I have heard similar statements to yours, but I have no reason at all to believe they are true. (I'm assuming you're talking about something quantum related, since statements like this seem to arise frequently from people (mis?)interpreting the subject) –  Eric Stucky Jun 27 '12 at 3:27
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And Nicholas, I probably should say this: I'm pretty good at reading mediocre-to-poor English and quite patient about trying to parse it out. In general you should not expect this. Your current wording of the question is reasonably good, but your wording of the statement you were told is almost incomprehensible. I could be wrong, but I would assume this is the reason for the downvotes. –  Eric Stucky Jun 27 '12 at 3:43

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