Math formulas: Numbers sets

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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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