Summary of notations — lesson. Mathematics State Board, Class 9.

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Consider the set of all natural numbers.

Roster form of the set:

A = \{1, 2, 3, 4, 5, ...\}

Set builder form:

A = \{x : x is a natural number}

Thus, it can be concluded that $1, 2, 3,...$ are belongs to the set $A$.

But the element $0$ doesn't belongs to the set $A$.

Here comes the list of symbols we often use to denote the sets.

Symbol	Meaning	Example
$\in$	belongs to	Suppose $A = {3, 4, 5}$ then $3$ $\in$ $A$.
$\notin$	does not belongs to	Suppose $A = {3, 4, 5}$ then $6$ $\notin$ $A$.
$:$ or $\|$	such that	The set builder form $A = {3, 4, 5}$ is $A = {x : x is a natural number, 3 \leq x \leq 5\}$
$ℕ$	the set of all natural numbers	$ℕ = {1, 2, 3, ...}$
$W$	the set of all whole numbers	$W = {0, 1, 2, 3,...}$
$ℤ or I$	the set of all integers	$ℤ = {..., - 3, - 2, - 1, 0, 1, 2, 3, ...}$
$ℤ +$	the set of all positive integers	$ℤ + = {1, 2, 3, 4, ...}$
$ℚ$	the set of rational numbers	$ℚ = {\frac{p}{q}, q \neq 0 with p and q are integers\}$
$ℚ +$	the set of positive rational numbers	$ℚ + = {\frac{p}{q}, q \neq 0 with p and q same sign integers\}$
$ℝ$	the set of real numbers	$ℝ = {x \| - \infty \leq x \leq \infty}$
$ℝ +$	the set of positive real numbers	$ℝ + = {x \| 0 < x \leq \infty\}$

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4. Summary of notations