Let $S_{1},S_{2},S_{3},....$ be a sequence of mathematical statements, each of which is dependent on the same variable, such that, at any given moment exactly one and only one of the statements can be true, while the others must be false. What's a mathematical term for this condition on the sequences $S_i$?
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you mean like the two statements A = "The sun is in the sky" and B = "The sun is not in the sky", which are both dependent on the variable sun? – Coffee_Table Apr 22 '13 at 01:21
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@Coffee_Table yes, and they are both such that only one can be true, ie we can't have the sun in the sky, and not in the sky, it must be one or the other, I was looking up stuff with key words like 'zero one law', but I can't find anything. – Ethan Splaver Apr 22 '13 at 01:24
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Do you mean there is one variable on which the truth of each is dependent, or for each, there is one variable on which each is dependent? The way you've phrased it is $\forall...\exists...$, but if you mean $\exists...\forall..$ then I'll delete my answer. – amWhy Apr 22 '13 at 01:25
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That would be a "trichotomy" of sorts... – amWhy Apr 22 '13 at 01:37
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@amWhy lol disregaurd that post where I said disregaurd, I am sorry for making things so complicated, the way the question is now, is exactly what I want, I would give your answer more thumbs up, if I could, because I really appreciate your time. – Ethan Splaver Apr 22 '13 at 01:40
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Don't fret, Ethan. Complicated ideas can be complicated to express! Not that I mean anything negative by "complicated"...just a challenge to grasp, intuitively. ;-) – amWhy Apr 22 '13 at 01:42
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Edit: If at most one of a collection of statements $S_i$ is true, we can say that the $S_i$ define conditions that are mutually exclusive, and if at least one of a collection of statements $S_i$ is true, we can say that the $S_i$ define conditions that are mutually exhaustive (although I have never used this second term myself).
Qiaochu Yuan
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