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Null sets : P

  1. Apr 25, 2004 #1
    Wot exactly is a null set? i dont understand it. if anyone could explain that wuld be wikid. :cool:
     
  2. jcsd
  3. Apr 25, 2004 #2

    matt grime

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    it would depend on the context, but it is, generically, something that is zero.
     
  4. Apr 25, 2004 #3
    It exists to make difference between "something" and "nothing". A set that contains something is like something and the null set is nothing (contains nothing)
     
  5. Apr 25, 2004 #4

    matt grime

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    No, that is not necessarily true. A null set, could be, as I suspect it will be in this case, a set of measure zero.
     
  6. Apr 25, 2004 #5
    ok..maybe my english is not good enough.. what is that called: ø?
     
  7. Apr 25, 2004 #6
    isn't it a null set? or an empy set?
     
  8. Apr 25, 2004 #7

    matt grime

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    that is the empty set. It is a null set in the sense that its cardinality is zero.
     
  9. Apr 25, 2004 #8
    is there any other set, whiches cardinality is zero exept the empty set?
    I don't think so
     
  10. Apr 25, 2004 #9

    matt grime

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    No, it, the empty set, is unique. But that doesnt' have any bearing on what a null set is until we see what situation we are dealing with.
     
  11. Apr 26, 2004 #10
    For example.. the set of rationals and irrationals. rationals are a null set and wot bout irrationals?? Matt could u explain in dummy maths why rationals are a null set?
     
  12. Apr 26, 2004 #11

    matt grime

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    As I thought, a null set is one that has measure zero. Example: and countable subset of R (Eg the rationals): let x_i be an enumeration of the set, round each point x_i consider the interval e/2^i, then the measure of the set is less than the sum over i of e^2^i = e. e was arbitrary hence it has measure zero.
     
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