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16th April 2012, 11:57 AM | #41 |
Extrapolate!
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I don't really understand what it is you're after. Mathematically, probability is described by probability theory and possibility/necessity by modal logic. Those are very different things.
: "p is possible if, and only if, it is not necessary that not-p." Possibility and necessity (let's call them M and L in text) act like quantifiers rather than values, and formally behave very analogously to existential and universal quantifiers: : "there exists an x such that Px if, and only if, it is not the case that for all x, Px is false." There is no reason why a probability space can't include impossible events. If I roll a standard die, there is no possibility of getting a 10. That can be put in the probability space without any trouble. And technically, the empty set is an event that is in many situations not possible. |
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16th April 2012, 12:26 PM | #42 |
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This is not quite true. It is possible to flip a fair coin an infinite number of times and have it come up heads every time. Yet the probability is zero.
http://en.wikipedia.org/wiki/Almost_surely |
16th April 2012, 12:32 PM | #43 |
Illuminator
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16th April 2012, 12:41 PM | #44 |
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16th April 2012, 06:41 PM | #45 |
Penultimate Amazing
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"That is a very graphic analogy which aids understanding wonderfully while being, strictly speaking, wrong in every possible way." —Ponder Stibbons |
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17th April 2012, 10:48 PM | #46 |
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18th April 2012, 12:14 AM | #47 |
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If you think anything's possible, try winning a game of Chess with your first move.
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18th April 2012, 03:06 AM | #48 |
Critical Thinker
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If your opponent concedes?
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18th April 2012, 07:13 AM | #49 |
Penultimate Amazing
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"Reality is what's left when you cease to believe." Philip K. Dick |
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18th April 2012, 07:14 AM | #50 |
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"Reality is what's left when you cease to believe." Philip K. Dick |
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