# List of Formulas related to Sets of Numbers

## Definitions:

 $\mathbb{N}$ : Natural numbers, $\mathbb{N}_0$ : Whole numbers, $\mathbb{Z}$ : Integers, $\mathbb{Z}^+$ : Positive integers, $\mathbb{Z}^-$ : Negative integers, $\mathbb{Q}$ : Rational numbers, $\mathbb{C}$ : Complex numbers

### Formulas:

Natural numbers (counting numbers ) $\mathbb{N} = \left\{ 1, 2, 3, \dots \right\}$ Whole numbers ( counting numbers with zero ) $\mathbb{N}_0 = \left\{0, 1, 2, 3, \dots \right\}$ Integers ( whole numbers and their opposites and zero ) $\mathbb{Z} = \left\{ \dots , -2, -1, 0, 1, 2, \dots \right\}$ $\mathbb{Z}^+ = \mathbb{N} = \left\{ 1, 2, \dots \right\}$ $\mathbb{Z}^- = \left\{ \dots , -3, -2, -1 \right\}$ $\mathbb{Z} = \mathbb{Z}^- \cup { 0 } \cup \mathbb{Z}$ Irrational numbers: Non repeating and nonterminating integers
Real numbers: Union of rational and irrational numbers
Complex numbers: $\mathbb{C} = \left\{ x+iy ~|~ x \in \mathbb{R} ~~ and ~~ y \in \mathbb{R} \right\}$ $\mathbb{N} \subset \mathbb{N}_0 \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}$