Math Calculators, Lessons and Formulas

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Math Formulas: 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:

 $$\mathbb{C} = \left\{ x+iy ~|~ x \in \mathbb{R} ~~ and ~~ y \in \mathbb{R} \right\}$$
 $$\mathbb{N} \subset \mathbb{N}_0 \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}$$

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