Definitions:

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\[\mathbb{N}\]	: 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:

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