Algebra 2 Honors - Sets of Real Numbers and Properties

Vocabulary flashcards covering sets of real numbers, their definitions, examples, and the properties of addition and multiplication.

Natural or Counting Numbers

$$N = \{1, 2, 3, \dots\}$$

Whole Numbers

$$W = \{0, 1, 2, 3, \dots\}$$

Integers

$$Z = \{\dots, -2, -1, 0, 1, 2, \dots\}$$

Rational Numbers

$$Q = \text{any number that is a terminating OR repeating decimal (examples: } 0.5\text{, } \frac{1}{3}\text{, } -0.312\text{, } 9\text{)}$$

Irrational Numbers

$$I = \text{any number that is a non-terminating AND non-repeating decimal (examples: } \sqrt{2}\text{, } \pi\text{, } -3.161661666\dots\text{)}$$

Real Numbers

$$R = \text{all numbers}$$

Closure Property

Addition: $a + b \text{ is } R$; Multiplication: $ab \text{ is } R$

Commutative Property

Addition: $a + b = b + a$; Multiplication: $ab = ba$

Associative Property

Addition: $(a + b) + c = a + (b + c)$; Multiplication: $(ab)c = a(bc)$

Identity Property

Addition: $a + 0 = a$; Multiplication: $a \cdot 1 = a$

Inverse Property

Addition: $a + (-a) = 0$; Multiplication:

$$a \cdot \frac{1}{a} = 1\text{, if } a \neq 0$$

Distributive Property

$$a(b + c) = ab + ac$$

Subtraction

Simply adding the "opposite"

Division

Simply multiplying by the "reciprocal"