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Sarah_Miller720 Group Title

Suppose U = {1, 2, 3, 4, 5, 6, 7, 8} is the universal set and P = {1, 2, 3, 4}. What is P'?

  • one year ago
  • one year ago

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  1. Sarah_Miller720 Group Title
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    i forgot how to do this stuff so i need some help :)

    • one year ago
  2. Sarah_Miller720 Group Title
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    my choices. {5, 6, 7, 8} {1, 2, 3, 4, 5, 6, 7, 8} {1, 2, 3, 4} cannot be determined

    • one year ago
  3. mivanov Group Title
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    well the first thing is that a universal set contains all sets including itself. for most set axiomatics you must know that such set does not exists, because of a paradox. Although there are some set axiomatics for which it exists

    • one year ago
  4. mivanov Group Title
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    Also for it be the universal set you can't say it has just 8 elements :D this is just plain not right

    • one year ago
  5. JayDS Group Title
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    Universal meaning "everything" so it must be everything inside P and also U.

    • one year ago
  6. mivanov Group Title
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    if we say that U is just a set(not the universal one) then we can say that P is a proper subset of U

    • one year ago
  7. mivanov Group Title
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    If a universal set exists, it's not a countable set. You should check out some set theory. It's cool.

    • one year ago
  8. JayDS Group Title
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    Universal meaning "everything" so it must be everything inside P and also U, excluding any reptitions.

    • one year ago
  9. JayDS Group Title
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    lol, u know ur theory stuff @mivanov , seems like u need to teach me some :)

    • one year ago
  10. mivanov Group Title
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    So you can't just list it's elements casually like that :D. And for most set theory axiomathics such set does not exists because of a simple paradox anyway.

    • one year ago
  11. Sarah_Miller720 Group Title
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    So since i need everything then my answer would be{ 1, 2, 3, 4, 5, 6, 7, 8} right?

    • one year ago
  12. JayDS Group Title
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    yes u are right.

    • one year ago
  13. mivanov Group Title
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    thank you. Well there are 3 types of sets -> countably finite ex. {a,b,c} it has 3 elements because we can have bijective function f: {1,2,3} -> {a,b,c} that is for each element we can numerate it with a natural number. and the set {1,2,3} is the set of all numbers bellow or equal to 3. Second we have countably infinite sets. Imagine A is a set. If we can have a function f: N -> A such that it's bijective,(for each element of A there is unique element from N and the opposite is true as well) we call the set countably infinite. And last we have sets which are countably infinite. Example is the set of all subsets of the natural numbers. Such a set is called a power set. Namely for N it's writen P(N). The proofs of these statements aren't that long, if you are interested you can look around and read them.

    • one year ago
  14. mivanov Group Title
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    and if a universal set P exists, then we have that P is an element of P, also any elements composed of empty sets. Because the empty set is a subset of every set. Example we would have that {empty set} is an element of P, {{empty set}}, basically it has an infinite number of elements, and can't be comprehended easily. Also it leads to a paradox, because we have another axiom that tells us that for each property E(x) exists a set A for which the elements of A posses that property. It's called the Russel paradox.

    • one year ago
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