1.1 - Real Numbers

Real Numbers are very simply put as numbers that exist, but there are many different classifications of real numbers.

Types of Real Numbers

Real numbers can either be rational or irrational.
Rational Numbers are numbers that can be written as a/b, when a and b are integers and b ≠ 0.
Irrational Numbers are non-terminating and non-repeating decimals.
Rational Numbers can then be either Fractions/Decimals or Integers.
Fractions/Decimals are not full numbers, such as -9, 0, or 7.
Integers are positive and negative whole numbers.
Integers can then be either Negative Integers (Opposites of Wholes) or Whole Numbers.
Negative Integers include -1, -2, -3, -4 and so on.
Whole Numbers include 0, 1, 2, 3 and so on.
Lastly, Whole Numbers can then be defined as Zero or Natural.
Zero only includes the number 0.
Naturals include 1, 2, 3, 4, and so on.

Properties of Real Numbers:

Commutative Property:
The commutative property states that "Order is immaterial when adding or multiplying two numbers"
a + b = b + a and ab = ba


Associative Property:
The associative property states that "Grouping is immaterial when adding or multiplying three numbers"
(a + b) + c = a + (b + c) and (ab) c = a (bc)


Identity Property:
The identity property states that "Adding 0 to any number or multiplying any number by 1 yields the same number"
a + 0 = a and a * 1 = a


Inverse Property:
The inverse property states that "Adding and number and its negative yields 0 and multiplying a nonzero number by its reciprocal yields 1"
 


Distributive Property:
The distributive property states that "Multiplying a number and a sum of two numbers is equivalent to multiplying each of the two numbers by the number and then adding the products"
a (b +c) = ab + ac and (a + b) c = ac + ab



Thanks and good luck,
Jacob