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Null set minus null set

  1. Oct 3, 2012 #1
    What is ∅-∅ equal to?
    Logically this is represented as the set containing all x such that x[itex]\in[/itex]∅ and x[itex]\notin[/itex]∅. I am confused on how to interpret this...I think the answer would just be the null set, but I am not sure. Could someone please clarify this?
     
  2. jcsd
  3. Oct 3, 2012 #2
    Think of the subtraction of sets as the intersection of the one with the complement of the other. That is ∅[itex]\cap[/itex] ∅[itex]^{c}[/itex]
     
  4. Oct 3, 2012 #3

    vela

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    There is no ##x## for which ##x \in \emptyset## and ##x \notin \emptyset##, so there are no elements in ##\emptyset - \emptyset##.
     
  5. Oct 3, 2012 #4

    Mark44

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    Makes me think of the song quite a few years back, "Nothin' from nothin' leaves nothin." - Billy Preston, 1975
     
  6. Oct 3, 2012 #5

    SammyS

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    Great post, Mark !
     
  7. Oct 3, 2012 #6

    Mark44

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    :approve:
     
  8. Oct 3, 2012 #7

    Hurkyl

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    That is exactly right. It may help to simplify that logical expression, because you can, for example, replace [itex]x \in \emptyset[/itex] with a truth value.

    Or maybe slightly reorganizing it to the fact that

    x is in ∅-∅​

    is synonymous with

    x[itex]\in[/itex]∅ and x[itex]\notin[/itex]∅​
     
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