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Math Help - Is a set the union of its finite subsets?

  1. #1
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    Is a set the union of its finite subsets?

    Hi:
    Let A be a set. Is A the union of all its finite subsets? By the way: how can I write a capital cursive in Latex? Regards and thanks for reading.

    Enrique.
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  2. #2
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    I would say yes it is. A union is everything included in the selected sets. Here, there is only one set, and we are not excluding any part of it, so it is in Union of itself. I am no expert., just trying to help.
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  3. #3
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    Quote Originally Posted by ENRIQUESTEFANINI View Post
    Hi:
    Let A be a set. Is A the union of all its finite subsets? By the way: how can I write a capital cursive in Latex? Regards and thanks for reading.
    Consider this very carefully.
    \bigcup\limits_{n \in A} {\{ n\} }  = ?

    [tex]A~,~\mathcal{A}~,~\mathbb{A}[/tex] gives A~,~\mathcal{A}~,~\mathbb{A}
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  4. #4
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    It was very kind of you. A short time after writing I saw the key was considering the singletons. Best regards,

    Enrique.
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