All Maths Formulas

Algebra

$\mathbb{N}$ : 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

Natural numbers (counting numbers )

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

$\mathbb{N} = \left\{ 1, 2, 3, \dots \right\}$

Whole numbers ( counting numbers with zero )

N 0 = {0, 1, 2, 3, \dots}

$\mathbb{N}_0 = \left\{0, 1, 2, 3, \dots \right\}$

Integers ( whole numbers and their opposites and zero )

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

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

Z + = N = {1, 2, \dots}

$\mathbb{Z}^+ = \mathbb{N} = \left\{ 1, 2, \dots \right\}$

Z - = {\dots, - 3, - 2, - 1}

$\mathbb{Z}^- = \left\{ \dots , -3, -2, -1 \right\}$

Z = Z - \cup 0 \cup Z

$\mathbb{Z} = \mathbb{Z}^- \cup { 0 } \cup \mathbb{Z}$

Irrational numbers: Non repeating and nonterminating integers

Real numbers: Union of rational and irrational numbers

Complex numbers:

C = {x + i y | x \in R a n d y \in R}

$\mathbb{C} = \left\{ x+iy ~|~ x \in \mathbb{R} ~~ and ~~ y \in \mathbb{R} \right\}$

N \subset N 0 \subset Z \subset Q \subset R \subset C

$\mathbb{N} \subset \mathbb{N}_0 \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}$

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