-4 
-3 -2 
-1 0
½ 1 
2 3
4
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Negative real numbers
Zero(neither + or -) Positive real
numbers
|
-4 |
Set of Rational Numbers
Real numbers {Rational Numbers{Fraction / Integers{Whole numbers{Counting}, 0}} }
Real numbers {Irrational numbers}
Definition
Rational Numbers:
{fractions, whole numbers (
),
integers}
The set of rational numbers
is : Q={
| Equality
of Rationals: Definition
|
Equality
Theorem: n = nonzero integer
|
| Addition
of Rationals: Definition
|
Additive
Inverse Theorem:
|
Properties (Rational Numbers
Addition):
| Closure:
Fract.
X Fract. = Fract.
|
Cumutative:
|
| Associative:
|
Additive
Inverse:
|
| Identity:
|
| Theorem:Additive
cancellation
|
Opposite
of Opposite:
|
Subtraction:
Adding Opp.
(common / uncommon denominators) |
Multiplcation of Rational Numbers
Properties
(Rational Numbers Multiplication):
| Closure:
Fract.
X Fract. = Fract.
|
Cumutative:
|
| Distributive
of Multiplication / Addition:
|
Multiplication
Inverse: (Theorem)
Every ratitionals
|
| Identity:
|
Associative:
|
Division of Rational Numbers
Division of Rationals: Theorem
1. 
2.
3.
Ordering of Rationals:
Number line approach
Common-positive denominator a/b > c/d ifi a > c
Additive approach
Cross-Multiplication Theorem: (for b > 0 and d > 0)
(smiplest form: lowest term)
(note
-b
hard to interpret)
has a unique rationals 
such
that: (reciprocal)
