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Real Numbers

Definition: The union of the rational numbers and the irrational numbers is the set of real

numbers.

The sets that make up the real numbers are called subsets of the real numbers

Properties of Real numbers:

Addition:

1.

For all real a, b

a + b = b + a

Commutative:

2.

For all real a, b, c

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

Associative:

3.

There exists a real number 0 such that for every real a

a + 0 = a

Identity:

4.

For every real number a there exist a real number, denoted

Additive Inverse (Opposite):

(a), such that a + (–a) = 0

Multiplication:

1.

For all real a, b

ab = ba

Commutative:

2.

For all real a, b, c

(ab)c = a(bc)

Associative:

3.

There exists a real number 1 such that for every real a

a × 1 = a

Identity:

4.

For every real number a except 0 there exist a real

Multiplicative Inverse (Reciprocal):

number, denoted , such that a × = 1

Distributive Law

For all real a, b, c

a(b + c) = ab + ac, and (a + b)c = ac + bc.

Part 5: Exponents and Scientific Notation

0 :

Exponents properties (

∙

(product rule)

1.

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Parent category: Education