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Math Help - Set to Sequence

  1. #1
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    Set to Sequence

    Hi all,

    Give a sset, how can we convert that into a sequence? Like for example

    set S = { 1, 2, 3, 4 }
    seq S = < 1, 2, 3, 4 >

    thanks

    ssharish
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  2. #2
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    Re: Set to Sequence

    Quote Originally Posted by ssharish View Post
    Give a sset
    Is it a typo?

    Quote Originally Posted by ssharish View Post
    how can we convert that into a sequence?
    There are many ways to convert a set into a sequence. For an n-element set, n! ways, to be precise. Note that {1, 2, 3, 4} = {4, 3, 2, 1} as sets. If a set A has n elements, then any injection {1, ..., n} -> A can be considered a sequence of elements of A.
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  3. #3
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    Re: Set to Sequence

    Thanks a lot emakarov for the reply.
    Sorry yeah definitely that a typo. I do slip out of my typing now and then

    So from what youíre saying can the following be considered as a sequence?

    \{ e:\{1,2,3,4\}|\exists n:\mathbb{N} \bullet n \mapsto e \}

    And of course n \mapsto e is n injective function.

    thanks

    ssharish
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  4. #4
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    Re: Set to Sequence

    Quote Originally Posted by ssharish View Post
    \{ e:\{1,2,3,4\}|\exists n:\mathbb{N} \bullet n \mapsto e \}

    And of course n \mapsto e is n injective function.
    In regular mathematics, as opposed to type theory or programming, one uses ∈ instead of : . Next, the set {e ∈ {1,2,3,4} | ...} is just a subset of {1,2,3,4}, not a sequence.

    The question is about the meaning of the question "how can we convert that [a set] into a sequence?" Do you mean conversion in some formal system or programming language? Do you mean some mathematical expression for a sequence? In this case, it is good to have a precise definition of a sequence. Otherwise, converting a set into a sequence informally is easy: choose the order of elements and change { } into < >.
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  5. #5
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    Re: Set to Sequence

    I certainly mean mathematical expression.

    I'm involved in writing an function which gets just gets a set of elements from a set of relations.

    So what Iím really doing is writing a axiomatic definition or a function which takes a set and returns a sequence.

    I've already managed to get a set of elements which i will have to return it in terms of sequence. Hence the question.

    Not quite sure if that answers your question.

    thanks

    ssharish
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  6. #6
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    Re: Set to Sequence

    >Next, the set {e ∈ {1,2,3,4} | ...} is just a subset of {1,2,3,4}, not a sequence.

    And I also understand why use ∈ rather than ':'. I think thats how its been used in Z. Sorry about that. Although what i was doing there was a set comperhensin to create a set of mapletsto form a sequence given a set.

    thanks a lot

    ssharish
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