**Real Numbers (Numbers that Exists)**

### Natural Numbers

- include positive numbers
- do not include zero
- do not include negative numbers
- do not include decimals or fractions

*Examples*

**✓**1, 2, 3, 4

**✘**-2, 0, 2.5

### Whole Numbers

- includes positive numbers
- includes zero
- does not include negative numbers
- does not include decimals or fractions

*Examples*

**✓**0, 1, 2, 3, 4

**✘**-4, -1.5, 3.7

### Integers

- includes positive numbers
- includes zero
- includes negative numbers
- does not include decimals or fractions

*Examples*

**✓**-2, -1, 0, 1, 2

**✘**-4.3, -2.9, ½

### Rational Numbers

- any number that can be represented as a fraction

*Examples*

**✓**-3, 4.25, 0.004

**✘**√2, √3, π

### Irrational Numbers

- any number that cannot be represented as a fraction

*Examples*

**✓**√2, √3, π

**✘**3.14, 22/7

**Imaginary Numbers (Numbers That Don’t Exist)**

### Imaginary Numbers

- the square root (or even root) of a negative number
- squaring a negative number results in a positive number, thus the square root of a negative number does not exist
- generally represented as
*i*= √-1

*Examples*

**✓**√-2, 4√-25

**✘**√7, √19

### Complex Numbers

- includes a real part (
*a*) and an imaginary part (*bi*) - acts like a binomial in calculations
*a*+*bi*

*Examples*

**✓**4 + 3

*i*

**✘**x

^{3}– 3x = 14

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