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Math Help - Family of sets

  1. #1
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    Family of sets

    \mathcal{F}=\{\{1,2\}, \{3,4\},\{5,6\}\}

    \mathcal{F} is a family of sets.


    Question: Is \{\{2,8\}\} a family of set(s)? If not, is there a name for it?
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  2. #2
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    What's your definition of a "family of sets"? Is it just a "set of sets"? If the answer is 'yes', then of course {{2 8}} is a family of sets.

    /

    Sometimes, though, "family" has a more special meaning, which is "function" where the domain is called "the index set" and the range is called "the indexed set" [refer to Halmos's 'Naive Set Theory']. But, with that definition, your F is not a family.
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