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Set
A set is a collection of objects from a specified universe. A set can be described verbally, by list, or with setbuilder notation.

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.

Set complement
 the set of elements in the universal set U that are not elements of A.
 __
 A

Subset
A is a subset of B if, and only if, every element of A is also an element of B
AcB

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
AcB

Intersection
the set of elements common to both A and B
AnB

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

Universe
consists of the objects allowed into consideration for a set (symbol U)

Element
an object that belongs to the collection, or set

Natural number or Counting number
a member of the set (Symbol N)

Equal Set
when A and B have percisely the same elements
(A=B)

Empty Set
A set that has no elements in it and is written O

Disjoint
are tow sets that have no elements in common
(AUB = O)

Counterexample
an example which shows that a statement is false.

The types of numbers
 1. Ordinal Numbers
 2. Cardinal Numbers
 3. Nominal Numbers

Nominal Numbers or Identification
a sequence of digits used as a name or label
ex. an id number

Ordinal Numbers
Descires location in an ordered sequence with the words first, second, third, fourth, and son on, communicating the basic notion of "where"

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

Equivalence of sets
When there is a onetoone corresepondence of the elements of the two sets

OnetoOne 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

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.

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

Finite
a set that is either the empty set or a set wquivalent to (1,2,3...), for some natural number n

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.

Addition of whole numbers
a+b + n(AUB), where as a= n(A), b= n(B)

Closer property
the sum of two whole numbers is a w hole number

Commutative Property
For all whole numbers a and b, a+b= b+a

Associative Property
for all whole numbers a,b,c, a+(b+c) = (a+b) +c

Zero Properts of addition
zero is an additive identity, so a+0 = 0+a=a for all whole numbers a

Binary Operation
an operation in which tow whole numbers are combined to form antoehr whole number

Addition or Sum
the total number of a and b combined collection

Addends or summands
the expression a+b are a and b

difference
the unique whole number c such that a =b+c

minuend
in the expression ab...it is a

Subtrahend
i the expression ab it is b

Multiplication
a repeated addition, so that a*b = b+b...+b where the are a addends

factor
each whole number a and b of the product a*b

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

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.

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

Dividend
a/b; a is the divedent

divisor
a/b; b is the divisor

