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I need some help here .

  1. Jan 28, 2010 #1
    I need some help here .....

    I wont to know what the difference between the proper and improper subset ..... with examples .........
     
    Last edited by a moderator: Jan 28, 2010
  2. jcsd
  3. Jan 28, 2010 #2

    CompuChip

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    Re: I need some help here .....

    If you check the definition of a subset of some set X, you will find that also the empty set {} and X itself satisfy it.

    However, our intuition often says that a subset should really be "smaller" than X, for example, {1, 2, 3} should not be a subset of {1, 2, 3}, but {1, 2} should.

    This is what we try to capture in "proper subset". Mathematically, it is a non-empty subset not equal to the whole set.

    So {1, 2, 3} and {1, 2} are both subsets of {1, 2, 3}, but only {1, 2} is a proper subset
     
  4. Jan 28, 2010 #3
    Re: I need some help here .....

    thank you Mr. Compuchip ......


    but what about improper subset .......
     
  5. Jan 29, 2010 #4

    CompuChip

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    Re: I need some help here .....

    I never used that word.
    But apparently S is an improper subset of X if and only if S = X.
    (Personally, I would then also include the case of S being empty here).
     
  6. Jan 29, 2010 #5
    Re: I need some help here .....

    thank you again Mr . Compuchip ... thank you so much .......
     
  7. Jan 30, 2010 #6

    HallsofIvy

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    Re: I need some help here .....

    Some texts (I think the majority) use the phrase "proper subset of A" to mean any subset of A other than A itself. Other texts use the phrase to mean any subset of A other than A itself or the empty set.
     
  8. Jan 30, 2010 #7
    Re: I need some help here .....

    In another context, the set of divisors of an integer are called the aliquot parts, where the divisors are said to be "proper", i.e., the set does not include the number itself.

    Thus, the aliquot parts of 12 are {1,2,3,4,6}. 12 is not included as it is not a "proper" divisor.
     
    Last edited: Jan 30, 2010
  9. Jan 31, 2010 #8
    Re: I need some help here .....

    thank you again so much
     
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