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Thread: Basic Set theory...

  1. #1
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    Basic Set theory...

    What is the difference between

    $\displaystyle \subset$ and $\displaystyle \subseteq$

    Thank you very much
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  2. #2
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    A,B sets
    A $\displaystyle \subset$ B ---> this means that all elements from set A are also elements of set B where B is bigger set ( it has more elements (important) )
    A $\displaystyle \subseteq$ B ---> this means that all elements from set A are also elements of set B where A can be equal to B

    example: A = { 1, 2, 3 }

    B = { 1, 2, 3 }

    then this is true: A $\displaystyle \subseteq$ B , but this isnt A $\displaystyle \subset$ B

    but if B is = { 1, 2, 3, 4 }

    A $\displaystyle \subseteq$ B is true and this is also true A $\displaystyle \subset$ B
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  3. #3
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    You may not be pleased with this answer.
    There is no precise difference; it generally depends upon the author and the textbook.
    In general, $\displaystyle \subset $ stands for a proper subset and in that case this symbol $\displaystyle \varsubsetneq $ is also used.
    That is, it is a subset but not the entire superset.

    For example, all of the following are correct usage:
    $\displaystyle \left\{ {1,2,3} \right\} \subset \left\{ {1,2,3,4,5} \right\},\;\left\{ {1,2,3} \right\} \varsubsetneq \left\{ {1,2,3,4,5} \right\}\left\{ {1,2,3} \right\} \subseteq \left\{ {1,2,3,4,5} \right\}$

    To be clear as to a set being a proper subset it is best to use this $\displaystyle A \varsubsetneq B$.
    That makes it clear that $\displaystyle A$ is not $\displaystyle B$.
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  4. #4
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    Thanks very much :]

    I'll thank you both

    :]
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