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Math Help - Why is this true ?

  1. #1
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    Why is this true ?

    In ordered structures, the book says that

    A^1 != A

    In the example, they say :

    Let A = {a,b,c}

    A^1 = { (a) , (b), (c) }

    How does the parentheses make them different ?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Matter_Math View Post
    In ordered structures, the book says that

    A^1 != A

    In the example, they say :

    Let A = {a,b,c}

    A^1 = { (a) , (b), (c) }

    How does the parentheses make them different ?
    Firstly, saying A^1 != A is not a good practice on a math website. We don't do C++ here, it's A^1\ne A. And, although I have actually not seen this notation before my gut tells me that it means A^1=\left\{\{a\}:a\in A\right\} which clearly, set theoretically that is, is not equal to A.
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  3. #3
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    Quote Originally Posted by Drexel28 View Post
    Firstly, saying A^1 != A is not a good practice on a math website. We don't do C++ here, it's A^1\ne A. And, although I have actually not seen this notation before my gut tells me that it means A^1=\left\{\{a\}:a\in A\right\} which clearly, set theoretically that is, is not equal to A.

    Oh thanks. I am new to formating words, sorry.

    A^1=\left\{\{a\}:a\in A\right\}

    This is the same in my book. Does that read, A^1 equals the all the
    pair (a) in which a is a element in A ?


    Sorry I am new to this completely.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Matter_Math View Post
    Oh thanks. I am new to formating words, sorry.

    A^1=\left\{\{a\}:a\in A\right\}

    This is the same in my book. Does that read, A^1 equals the all the
    pair (a) in which a is a element in A ?


    Sorry I am new to this completely.
    It's no problem. I have no idea what your book means. I would interpret it like this. A^1 is the set of all singletons in \wp\left(A\right). In other words, take each element of A put it in it's own set and then put it back. And as sets we have that a\ne\{a\}.
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  5. #5
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    Quote Originally Posted by Matter_Math View Post
    This is the same in my book. Does that read, A^1 equals the all the pair (a) in which a is a element in A ?
    Who is the author to your text book and what is the course name?
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  6. #6
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    Quote Originally Posted by Plato View Post
    Who is the author to your text book and what is the course name?

    The above was not stated in the book, it was by bad interpretation, sorry.

    My book is called : Discrete Structures, Logic , and Computability
    by James L. Hein, 3rd edition.

    and the course name is called Discrete Systems.
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