Math Chp. 2

  1. Set
    A set is a collection of objects from a specified universe. A set can be described verbally, by list, or with set-builder notation.
  2. Venn Diagram
    Where the universe is a rectangle and closed loops inside the universe correspond to sets. Elements of a set are assocaited with points within the loop corresponding to that set.
  3. Set complement
    • the set of elements in the universal set U that are not elements of A.
    • __
    • A
  4. Subset
    A is a subset of B if, and only if, every element of A is also an element of B

  5. Proper Subset
    A is a proper subset of B when AcB, but there must be some element of B that is not also an element of A. A does not equal B

  6. Intersection
    the set of elements common to both A and B

  7. Union
    the set of all elements that are in A or B

  8. Universe
    consists of the objects allowed into consideration for a set (symbol U)
  9. Element
    an object that belongs to the collection, or set
  10. Natural number or Counting number
    a member of the set (Symbol N)
  11. Equal Set
    when A and B have percisely the same elements

  12. Empty Set
    A set that has no elements in it and is written O
  13. Disjoint
    are tow sets that have no elements in common

    (AUB = O)
  14. Counterexample
    an example which shows that a statement is false.
  15. The types of numbers
    • 1. Ordinal Numbers
    • 2. Cardinal Numbers
    • 3. Nominal Numbers
  16. Nominal Numbers or Identification
    a sequence of digits used as a name or label

    ex. an id number
  17. Ordinal Numbers
    Descires location in an ordered sequence with the words first, second, third, fourth, and son on, communicating the basic notion of "where"
  18. Cardinal Number
    the number of objects in the set, communicating the basic notion of "how many"

    ex. there are 9 justices of the U.S supreme court
  19. Equivalence of sets
    When there is a one-to-one corresepondence of the elements of the two sets
  20. One-to-One Correspondence
    each element of one set is paired with exactly one element of another set,and each element of either set belongs to exactly one of their pairs
  21. Whole Numbers
    the cardinal numbers of finite sets, with zero bieng the cardinal number of the empty set. they can be represented and visualized by a varitey of manipulatives and diagrams.
  22. Order of the whole numbers
    M is less than N if a set with M elements is a proper subset of a set with N elements
  23. Finite
    a set that is either the empty set or a set wquivalent to (1,2,3...), for some natural number n
  24. Infinite
    a set that is not finite. One way to think of an infinite set is that, if you were to list all memebers of the set the list would go on forever.
  25. Addition of whole numbers
    a+b + n(AUB), where as a= n(A), b= n(B)
  26. Closer property
    the sum of two whole numbers is a w hole number
  27. Commutative Property
    For all whole numbers a and b, a+b= b+a
  28. Associative Property
    for all whole numbers a,b,c, a+(b+c) = (a+b) +c
  29. Zero Properts of addition
    zero is an additive identity, so a+0 = 0+a=a for all whole numbers a
  30. Binary Operation
    an operation in which tow whole numbers are combined to form antoehr whole number
  31. Addition or Sum
    the total number of a and b combined collection
  32. Addends or summands
    the expression a+b are a and b
  33. difference
    the unique whole number c such that a =b+c
  34. minuend
    in the expression is a
  35. Subtrahend
    i the expression a-b it is b
  36. Multiplication
    a repeated addition, so that a*b = b+b...+b where the are a addends
  37. factor
    each whole number a and b of the product a*b
  38. Repeated addition Model
    A way to represent the multiplication operation; where a and b are any two whole numbers, a multiplied by b, written a*b, is defined by a*b = b+b....+b with a addends, when a is not zero and by 0*b
  39. Ordered pair
    the prepersentation of the first component,a, form one set and a second component, b, from anotehr set. It also indicates the Cartesain coordiantes of a point.
  40. Cartesian Product
    (AxB) the set of all ordered pairs whose first component is an element of set A and whose second componenet is an element of set B
  41. Dividend
    a/b; a is the divedent
  42. divisor
    a/b; b is the divisor
Card Set
Math Chp. 2
Sets and Whole Numbers