Notation

Sets of Numbers

$$\N = \text{Set of natural numbers} = \{ 0;1;2;3; ... \}$$ $$\Z = \text{Set of integers} = \{ ... ; -3 ; -2 ; -1 ; 0 ; 1 ; 2 ; 3 ; ... \}$$ $$\mathbb{Q} = \text{Set of rational numbers} = \left\{ \frac{a}{b}~\text{such that}~a \in \Z \text{,}~b \in \Z~\text{and}~b \ne 0 \right\}$$ $$\R = \text{Set of real numbers}$$ $$\mathbb{C} = \text{Set of complex numbers}$$ $$~~~~~~~\text{Let A be a set of real numbers}$$ $$\mathbb{R} \setminus A = \text{Set of real numbers excluding all real numbers that belong to A}$$ $$\R^* = \text{Set of nonzero real numbers} = \R \setminus \{ 0 \}$$ $$\mathbb{R}^+ = \text{Set of positive real numbers}$$ $$\R^- = \text{Set of negative real numbers}$$

Intervals

$$\lbrack a ; b \rbrack~\text{Set of all real numbers between a and b, including the endpoints a and b.}$$ $$\text{This is called the "closed interval a, b".}$$ $$\rbrack a ; b \lbrack~\text{Set of all real numbers between a and b, excluding the endpoints a and b.}$$ $$\text{This is called the "open interval a, b".}$$ $$\lbrack a ; b \lbrack~\text{Set of all real numbers between a and b, including a and excluding b.}$$ $$\text{This is called the "half-open interval closed at a, open at b".}$$

Some Symbols

$$\forall~\text{for all}$$ $$\exists~\text{there exists}$$ $$\in~\text{belongs to}$$