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How can B be an element of C?

  1. Oct 26, 2013 #1
    Question 2 (a)

    how is it possible? B is a set (since A is a set), how can a set be an element of another set?

    Rather than saying: B is an element of C

    I thought it would be better to say: B is a subset of C.

    Also, can someone explain question 2 (d) to me? thanks

    Attached Files:

  2. jcsd
  3. Oct 26, 2013 #2
    im quite desperate.
  4. Oct 26, 2013 #3


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    Yes, a set can be an element of another set. There may be a set X={a,b,c}, where X is an element of Y.
    But neither a, nor b, nor c becomes a member of Y; only the sets are members.

    But you can have a set Z = {a, X} ... so X contains a,b,c, but neither b nor c is a member of Z.

    Sets are "packages", and the set Z has the package X as an element - like having an apple and a package of sausages in your shopping bag. You can reach in and pull out the apple, but you cannot pull out a sausage - only a package of sausages.

    But you could reach into that package of sausages and pull out a sausage!
  5. Oct 26, 2013 #4


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    2(d) is the null set. Try it with the package concept!
  6. Oct 26, 2013 #5
    Great explanation, I understand now, thanks.

    But how would I go about 2 (d)? we have the empty set, {}:

    {A} = { { 0, {}, {{}} } }

    Judging by what you said, I don't see how {} can be related to the above set? it is neither an element nor a set.
  7. Oct 26, 2013 #6
    {} = sausages
    {{}} = packet of sausages
    0 = Orange

    { 0, {}, {{}} } = Shopping bag of (Orange + sausages + Packet of sausages).

    { { 0, {}, {{}} } } = car boot of Shopping bag.

    We want {{}} i.e. the packet of sausages. It is not related to the Car boot because it is neither a SET nor a MEMBER of the Car boot, it is too deep inside.
    Last edited: Oct 26, 2013
  8. Nov 2, 2013 #7


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    By the way, this is true in "Naive set theory" which suffers from "Russel's Paradox". In "class theory" we do NOT allow "sets" to be contained in sets, but have a hierarchy of "classes" in which classes in one tier can be contained in classes of a higher tier. "Sets" are the lowest tier of classes.
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