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Math Help - What set is the set I?

  1. #1
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    What set is the set I?

    I'm reading a book at the moment and it mentions a set I but doesn't define what this set is. Is there a general meaning for this set I?

    I'll post the context as it may be helpful

    Let X to be generated from f(x) where  x \in I

    Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by alan4cult View Post
    I'm reading a book at the moment and it mentions a set I but doesn't define what this set is. Is there a general meaning for this set I? I'll post the context as it may be helpful
    Let X to be generated from f(x) where  x \in I
    There is absolutely to give a firm answer to your question.
    If I were to guess, I would say that \mathscr{I} stands for the irrational numbers.
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  3. #3
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    There is absolutely to give a firm answer to your question.
    I think you accidentally the whole sentence.

    I think that I is some arbitrary index set, as in: Consider a family of subsets of natural numbers \{A_i\}_{i\in I}. That's why the author must have forgotten to describe it.
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  4. #4
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    The (closed) unit interval is often denoted by I, and from your context I feel this is most likely. That is, the set of real numbers between 0 and 1 inclusive, [0, 1].

    If not, my second guess would be an index set; I've never seen the complex numbers denoted by I (although that doesn't rule it out).

    Also, have you tried looking for a `notation' section in your book? They're often at the back with the index and references, or immediately after the contents.
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  5. #5
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    I've checked the book and it doesn't define I anywhere. An interval would make sense if we wanted to sample only x's that fall with in the interval I, however I think it maybe an arbitrary interval rather than [0,1]
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  6. #6
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    If you post more about the context, maybe we can recognize its use.
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  7. #7
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    The context is the Acceptance-Rejection Method in Random Variable Generation. X is the variable I wish to sample and it has probability distribution f(x), x \in I
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