Math 13 Ch2

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Mattyj1388
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158264
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Math 13 Ch2
Updated:
2012-10-23 12:48:31
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Libral Arts math013 COD
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  1. Set
    • A "Set" is a collection of objects. We use the symbols {} to indicate that the collection is a set.
    • Example:
    • N = {1, 2, 3, 4, 5, . . . .}
  2. Element
    • An element is a member of a set. We use the symbol ϵ (is an element of) to indicate when an element belongs to a set.
    • Example:
    • 3 ϵ {1, 2, 3, 4, 5, . . . }
  3. What does each symbol look like?
    Set =
    Element =
    Natural#'s =
    Whole #'s =
    Intagers =
    Rational #'s =
    • Set = {}
    • Element = ϵ
    • Natural#'s = N
    • Whole #'s = W
    • Intagers = I
    • Rational #'s = Q
  4. N =
    • N = Natural #'s or
    • {1, 2, 3, 4, 5, 6, . . . }
  5. W =
    • W = Whole #'s or
    • {0, 1, 2, 3, 4, 5, 6, . . . .}
  6. I =
    • I = Intagers or
    • {. . .-3, -2, -1, 0, 1, 2, 3, . . .}
  7. Q =
    • Q = Rational #'s or repeating/ending decimal value, or any fraction with intagers. Infanetly many points between to points.
    • Example:
    • Q={a/b|a ϵ I and b ϵ I and b ≠ 0}
  8. Well-defined set
    • A set is well-defined if we are able to tell whether any particular object is an element of the set.
    • Note: Q > I > W > N
  9. Null Set
    • The set that contains no elements is called the empty set or null set. This set is labeled by the or {} but not {}. {} means that an empty set is contained in an empty set. Every set has the empy set as a subset.
    • Note: = {} = Empty set
  10. Universal set
    The universal set is the set of all elements under consideration in a given discussion. We often denote the universal set by the capital letter U.
  11. Subset
    The set A is a subset of the set B if every element of A is also an element of B.
  12. Proper subset
    The set A is a proper subset of the set B if A B but AB.
  13. Sets containing subsets
    • A set can be a set of subsets.
    • Example:
    • Since N Q
    • and W Q
    • then NWQ
  14. Finite set
    • The number of subsets of a finite set can be found by finding the cardinal number of the set. A set that has k elements has 2k subsets.
    • Example:
    • A={(HH),(HT), (TH),(TT)} the set is finite and n(A) = 4. therefore 24 = 16 subsets.
    • Note: Pascals triangle to find subsets.
  15. Cardinal #:
    The Cardinal number is k in the finite set, or in other words, it is the total number of elements in the list.
  16. Equivalent Sets
    • Sets A and B are equivalent, or in One-to-One correspondence, if n(A) = n(B).
    • Example:
    • A={1, 2, 3, 4} ; B={a, b, c, d} then A and B are equivalent.

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