The formal definition of notation is defined as follows:
Notation is a symbol used for representing numbers, equations, elements or any mathematical sign or character, which has a particular meaning that conveys the procedure for solving any problem.
For example, if we want to solve a problem of adding 3 and 4, we can simply put the notation of addition, like 3 + 4 = 7, where '+' conveys the meaning that addition has to be performed. So, + symbol is used for the procedure of addition.Â Hence, in short, Notation is a symbol used for the procedure to solve any problem.
The following is a list of some common and basic notations used in mathematics:
NotationÂ 
Meaning of the symbolÂ 
ExampleÂ 
Â f(x) 
Symbol for s function of xÂ 
f(x) = 6x +Â 2Â 
Â (f o g) 
Symbol for the composition of the function denoted asÂ (f o g)(x) = f(g(x))Â 
f(x) = 6x, g(x) = x  2 then, (f o g)(x) = 6 (x  2) 
(a, b)Â 
Symbol for open interval denoted asÂ $(a,b) = {x:a  $x\epsilon (4, 10)$ 
[a, b] 
Symbol for closed interval denoted asÂ $[a,b] = {x:a\leq x\leq b}$

$x\epsilon [4,10]$ 
xÂ 
Symbol for the variable x, which is always an unknown quantity 
If 6x = 18, then x = 3Â 
$\equiv $Â 
Symbol for equivalenceÂ 
Like, 3 is identical to 3 
$\sim $ 
SymbolÂ for approximately equal to, which isÂ also known as weak approximation 
15$\sim $14.432

$\approx $Â 
Symbol for approximately equal to, whichÂ is proper approximation

sin(0.01) $\approx $ 0.01Â 
$\left  A \right $Â 
Symbol for determinant of matrix A 
determinant of matrix A 
det(A) 
Another symbol for determinant of matrix A 
determinant of matrix A 
$\left \ x \right \$Â 
Symbol for the Norm of a variableÂ 
$\left \ x \right \$ = x + 2Â 
B^{T}

Symbol for transpose of a matrix B 
$(B^{T})_{ij}=(B)_{ji}$ 
$B^{\div }$Â 
Symbol for the conjugate transpose of a matrixÂ B

$(B^{\div })_{ij}=(B)_{ji}$Â 
B^{*}

Another symbol for the conjugate transpose of a matrix B 
$(B^{*})_{ij}=(B)_{ji}$Â 
B^{1}

Symbol for the inverse of a matrix B 
BB^{1 }= I 
rank (B) 
Symbol for the rank of a matrix BÂ 
rank (B) = 3 
dim (B) 
Symbol for the dimension of a matrix BÂ 
rank (B) = 3 
In simple words, in mathematics, a notation is used as a short form by writing a symbol or sign, for conveying the meaning of a long sentence in short.Â
For example, if we want to write, that all the numbers from 0 to 20 are included, then instead of writing this whole sentence, we can just write it using the notation of closed parenthesis [Â ] as follows:
Hence, this notation of [0, 20] automatically conveys the meaning that all numbers from 0 to 20 are included, and on the other hand, if we want to write the numbers only above 0 and below 20, then we will simply use the notation of open parenthesis () as shown above, i.e., (0, 20).
Notations can be classified in accordance with, in which field of mathematics they are applied. Therefore, various types of notations can be as basic mathematical notations, geometric notations, algebraic notations, probability and statistical notations, set theory notations, logical notations, calculus and analysis notations, notations for the representation of system of numbers, notations of Greek symbols used for representing angles, notations for representing roman numbers etc.