# Math 13 Ch2

 The flashcards below were created by user Mattyj1388 on FreezingBlue Flashcards. 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, . . . .} 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, . . . } What does each symbol look like? Set = Element = Natural#'s = Whole #'s = Intagers = Rational #'s = Set = {}Element = ϵNatural#'s = NWhole #'s = WIntagers = IRational #'s = Q N = N = Natural #'s or{1, 2, 3, 4, 5, 6, . . . } W = W = Whole #'s or{0, 1, 2, 3, 4, 5, 6, . . . .} I = I = Intagers or{. . .-3, -2, -1, 0, 1, 2, 3, . . .} 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} 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 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 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. Subset The set A is a subset of the set B if every element of A is also an element of B. Proper subset The set A is a proper subset of the set B if A B but A ≠ B. Sets containing subsets A set can be a set of subsets.Example: Since N Qand W Qthen NWQ 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. Cardinal #: The Cardinal number is k in the finite set, or in other words, it is the total number of elements in the list. 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. AuthorMattyj1388 ID158264 Card SetMath 13 Ch2 DescriptionGeneral information Updated2012-10-23T16:48:31Z Show Answers