Chapter 1
1.1 Properties of Real Numbers
Real numbers – any # you can think of. From -∞ to +∞
Real Numbers
Irrational Numbers
Rational Numbers
```
Non Integer Rational
Integers
Negative Integers
Whole Numbers
Zero
Natural Numbers
Irrational Number – is any number that can be written as an infinite, nonrepeating decimal.
3 , 11
example = π, e,
Not a perfect square.
Decimal part does not repeat themselves.
Decimal part does not terminate.
Rational Number – is any number that can be written in the form a/b where a and b are integers and
b ≠ 0.
example = 3.14, 600, ¼, 3.13131313
Decimal part terminates.
Decimal part repeats itself.
Integers – Whole numbers from -∞ to +∞ with no fractional part.
example = -123, -122, …. -3, -2, -1, 0, 1, 2, 3, …. 122, 123, etc.
Non Integer Rational Numbers – all rational Numbers that are not integer.
example = -1/4, 8.75, 2/3, -.45
Negative Integers – from -∞ to -1, with no fractional parts.
example = -100, -99, …-3, -2, -1
Whole Numbers – Integer Numbers from 0 to +∞ with no fractional part.
example = 0, 1, 2, 3, ….100, 101, …..+∞
Natural Numbers – Integer Numbers from 1 to +∞ with no fractional part.
Inequality Symbols
<
>
≥
≤
less than
greater than
greater than or equal to
less than or equal to
Field Properties of Real Numbers
Addition
A1 a + b is a real number
Name of Property
Closure
Multiplication
M1 a * b is a real number
A2
a+b=b+a
Commutative
M2
a*b=b*a
A3
(a + b) + c = a + (b + c)
Associative
M3
(a * b) * c = a * (b * c)
A4
a+0=0+a=a
Identity
M4
a*1=1*a=a
A5
a + ( -a ) = 0
Inverse
M5
a * 1/a = 1 (a≠0)
D
Distributive Property
a * ( b + c ) = a * b + a * c or ( b + c ) * a = b * a + c * a
1.2 Operations with Real Numbers
Absolute Value
1. Distance between that number and zero.
2. A non negative number.
3. Non negative number always includes zero.
4. Use 2 vertical lines.
x  XX
if x is positive or 0, X = X ;
if x is negative,
if x  0
if x  0
Order of operations
Please Excuse My Dear Aunt Sally
1. ( )
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction
X = -X