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Subset ordering of sets

  1. Aug 26, 2006 #1
    I have seen the term "subset ordering of sets" at http://en.wikipedia.org/wiki/Order_theory

    What I can understand now is it is something related to the ordering of sets.

    But I can't understand literally what "subset ordering of sets" means.
    What is the subset, what are the sets, and how they relate to each other?
  2. jcsd
  3. Aug 26, 2006 #2


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    [itex]\subseteq[/itex] is a partial order. (on any class of sets)
  4. Aug 26, 2006 #3
    Thanks, but I still not really understand the whole picture.
    Can you please literally explain what is "subset ordering of sets"?
    Very thanks=)
  5. Aug 26, 2006 #4


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    In other words, a set A is considered less than or equal to a set B if A is a subset of B.
  6. Aug 26, 2006 #5


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    The "subset ordering" is [itex]A \le B[/itex] if and only if [itex]A \subseteq B[/itex]. If [itex]A \subseteq B[/itex] and [itex]B \subseteq C[/itex] then [itex]A \subseteq C[/itex]- the transitive property which is the only property required of an order relation.

    Are you saying that you don't understand what a "subset" is?
  7. Aug 26, 2006 #6
    Thanks, now I am getting clearer now=)
  8. Aug 27, 2006 #7


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    Notice that "trichotomy" does not hold: there may be sets A and B such that neither [itex]A\subseteq B[/itex] nor [itex] B\subseteq A[/itex] is true.

    (Trichotomy says: Given any A, B, one and only one of these must hold:
    1) A< B
    2) B< A
    3) A= B )
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