1. Real Numbers

Define a real number

Any number that can be plotted on a number line

Describe the categories that fall under real numbers

Irrational and rational > integers > whole numbers > natural numbers

Define a rational number (Q)

A number that can be written in the form of a ratio of two integers / any number that has the form p/q where q does not equal to 0

Define an integer (Z)

positive and negative numbers that are not fractions

Define whole numbers (W)

Positive intigers + 0

Define natural numbers

Positive intigers

List addition and multiplication properties of real numbers

• Closure

• Commutative

• Associative

• Identity

• Inverse 

• Distributive

Additive closure

a + b = c

Multiplicative closure

a x b = c

Additive commutative

a + b = b + a

multiplicative commutative

a x b = b x a

additive associative

a + ( b + c ) = ( a + b ) + c

multiplicative associative

a x ( b x c ) = ( a x b ) x c

Additive identity

a + 0 = a

Multiplicative identity

a x 1 + a

Additive inverse

a + ( - a ) = 0

Multiplicative inverse

if a does not equal to 0, a x 1/a = 1

Distributive

a ( b + c ) = ab + ac