Negative representations: (discuss historic and present international)

    Integers: set of numbers: {..,-3,-2,-1,0,1,2,3,..}

        Positive Integers, Zero, Negative Integers (Set View via models or
        Measurement view via the number line); concept of negative being opposite of
        positive across pivot point at Zero)

8.1 Addition & Subtraction:

    Set Model: Cancel effect: 4 positives + 3 negatives [i.e. 3 (-) cancels 3 (+) leaving 1 (+)]

    Number Line Model: a positives + b negatives: move from
        Zero a units right and then b units left from new position

    Addition Properties: (if a, b, c are integers)
 

Closure: a + b is an integer	Cumutative: a + b = b + a
Associative: (a + b) + c = a + (b + c)	Additive Inverse: a + (-a) = 0
Identity : a + 0 = a = 0 + a for all a

Theorem - Additive Cancellation for Integers: If a + c = b + c, then a = b

Theorem - Inverse of opposite:  - ( - a ) = a

8.2 Multiplication, Division, and Ordering Integers:

    If a and b are integers: 

           1. 
 

            2. 

            3. 

    Multiplication Properties: (if a, b, c are integers)
 

Closure: ab is an integer	Cumutative: a x b = b x a
Associative: (ab)c = a(bc)	Identity: a x 1 = a
Distribution: (Multipilcation over addition): a( b + c ) = ab + ac	Multiplication Cancellation: Ac = bc, then a = b
Zero Divisors: ab = 0, iff a = 0 or b = 0 or both = 0

Theorem - Multiplication by -1:  a (-1) = - a

Theorem - Multiplication of (-):  Case 1: (-a)b = -(ab)  Case 2: (-a)(-b) = ab

    Scientific Notation: An exponential representation of numbers in the form:

            Where a is called the mantissa and n the characteristic of exponent

    Ordering Integers Properties: (if a, b, c are integers)
 

Transitive Properties:  If a < b and b < c, then a < c	< addition: If a < b, then a + c < b + c
< Multiplication by (+): If a < b, then ac < bc	< Multiplication by (-): If a < b, then a(-c) > a(-c)

Use number line to order integers