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Basic Set Theory/Topology

  1. Dec 7, 2005 #1


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    The book that I'm reading is saying...

    If C is the null collection of subsets of S then,

    (Union) C = Null

    (Disjoint) C = S

    Is this true?
  2. jcsd
  3. Dec 7, 2005 #2
    How does your book define a null collection of subsets?
  4. Dec 7, 2005 #3

    matt grime

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    Take it as a definition, or read this, for example:


    since i presume by (disjoint) you actually mean intersection.

    incidentally i got that answer by insertingf the words empty intersection into google and clicking the first link.

    empty union requires you to follow the third (non indented) link.

    you might want to remember that the next time you struggle to check a definition,
    Last edited: Dec 7, 2005
  5. Dec 7, 2005 #4


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    The truth is that I searched and searched. Then I thought and thought, then searched again.

    Using the definition it is true, and I see that, but I was skeptical about it.

    Thanks, for the link.
    Last edited: Dec 7, 2005
  6. Dec 7, 2005 #5


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    imagine a list of rules for a game which has no rules at all!!

    the intersection of a null collection of sets, corresponds to those moves which satisfy all the rules, hence any move at all, i.e. S.

    etc....you do the other case
  7. Dec 31, 2005 #6
  8. Dec 31, 2005 #7


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    if x is in (Union)C, then it must be in at least one of the members of C. But C has no members so that is always false. Yes, (Union) C= Null set.

    By (Disjoint) C do you mean the intersection[\b] of all the members of C?

    Let x be any member of S. If x is NOT in (intersection) C, then there must be some member of C such that x is NOT in it. But that's NEVER true because C has no members! Therefore every member of S is in (Intersection) C.
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