Mathematical Symbols
Symbol 
What it is 
How it is read 
How it is used 
Sample expression 
+ 
Addition sign 
... plus ... 
Sum of a few values 
3 + 5 = 8 
* 
Multiplication sign 
... times ... 
Product of two values 
3 x 5 = 15 
x 
Multiplication sign 
... times ... 
Product of two values 
3 x 5 = 15 
· 
Multiplication sign 
... times ... 
Product of two values 
3 · 5 = 15 

summation sign 
The summation of ... 
Sum of many or 


Integral sign 
The integral of ... 
integration 
x^{2}
dx = x^{3}/3 + c 

double integral sign 
The double integral of
... 
integration 
f(x,y)
dx dy 

Triple integral sign 
The triple integral of
... 
integration 
f(x,y,z)
dx dy dz 

Line integral sign 
The line integral of
... 
integration 
F
dx 

Surface integral sign 
The surface integral of
... 
integration 
F(x,y,z)
dx dy 
 
Subtraction sign 
... minus ... 
Difference of two
values, 
3  5 = 2 
± 
Plus/minus sign 
... plus or minus ... 
Expression of range, 
500 kbps ± 10% 

Dot product sign 
... dot ... 
Scalar (dot) product 
A B
= B A 
x 
Cross product sign 
... cross ... 
Vector (cross) product 
A x B =  (B x A) 

Product sign 
The product of ... 
Product of three up to 

^ 
Carat 
... to the power of ... 
exponent 
2 ^ 5 = 32 
! 
Exclamation 
... factoriall 
Product of all positive 
5! = 120 

surd 
... root of ... 
Algebraic expressions 
z = (x
+ y) 

square root symbol 
The square root of ... 
Algebraic expressions 

... 
Continuation sign 
... and so on up to ... 
Extension of sequence 
S = {1, 2, 3, ...} 
/ 
Slash 
... divided by ... 
Division 
3/4 = 0.75 
÷ 
Division sign 
... divided by ... 
Division 
3 ÷ 4 = 0.75 
% 
Percent symbol 
... percent ... 
Proportion 
0.032 = 3.2 

Per mil symbol 
... per mil ... 
Proportion 
0.032 = 32 
: 
Colon, 
... is to ... 
Division or ratio, 
2:4 = 20:40 x
: x > 4 and x < 5 x
: x < 0 or x > 1 S = {x : x < 3} 
 
Vertical line 
... such that ... 
Symbol following 
x
 x > 4 and x < 5 x
 x < 0 or x > 1 S = {x  x < 3} 
:: 
Double colon 
... averaged with ... 
arithmetic mean 
3 :: 11 = 7 

lemniscate 
... infinity 
Infinite summations 
x : x
< 
( ) 
Parentheses 
...quantity... 
Denotes a quantity,
list, 
(x + y) +
z 
[ ] 
Square brackets 
... the quantity ... 
Denotes a quantity or a 
w + [(x + y)
+ z] 
( ] 
Hybrid brackets 
... the halfopen interval
... 
Denotes a 
(3,5] 
[ ) 
Hybrid brackets 
... the halfopen
interval ... 
Denotes a 
[3,5) 
{ } 
Curly brackets 
... the quantity ... 
Denotes a quantity or a
set 
E = {2, 4, 6, 8, ...} 
= 
Equal sign 
... equals ... 
Indicates two values 
(5) = 5 

Proportionality sign 
... is proportional to
... 
Indicates two variables 
x y 
~ 
Similarity sign 
... is similar to ... 
Indicates two objects
are 
ABC ~ DEF 

Approximate 
... is approximately
equal to ... 
Indicates two values
are 
x + y z 

Inequality sign 
... is not equal to ... 
Indicates two values 
x y 
< 
Inequality sign 
... is less than ... 
Indicates value on left 
3 < 5 

Inequality sign 
... is less than or
equal to ... 
Indicates value on left 
x y 
> 
Inequality sign 
... is greater than ...

Indicates value on left 
5 > 3 

Inequality sign 
... is greater than or
equal to ... 
Indicates value on left 
x y 
  
absolute value sign 
The absolute value of
... 
Distance of value from 
 3  = 3 

increment sign, 
the change in ... 
Indicates a small
change, 
m = y
/ x 

Perpendicularity 
... is perpendicular to
... 
Geometry 
L M 
// 
Parallel symbol 
... is parallel to ... 
Geometry 
L // M 

angle symbol 
Angle ... 
Geometry 
ABC
= DEF 

Existential quantifier 
For some ... 
Logical statements 
x
: x > 4 and x < 5 

Universal quantifier 
For all ... 
Logical statements 
x
: x < 0 or x > 1 
¬ 
Logical negation 
not ... 
Logical statements 
¬(¬A) A 

logical implication 
... implies ... 
Logical statements 
A B 

logical equivalence 
... is logically
equivalent to ... 
Logical statements 
A B 

Three dots 
... therefore ... 
Logical statements or 
x = y and y
= z 

Elementof 
... is an element of 
Sets 
a A 

Notelementof 
... is not an element
of 
Sets 
b A 

Subset symbol 
... is a subset of ... 
Sets 
A B 

Proper subset symbol 
... is a proper subset
of ... 
Sets 
A B 

Union symbol 
... union ... 
Sets 
A B = B A 

Intersection symbol 
... intersect ... 
Sets 
A B = B A 

Null symbol 
The null set 
Sets 
= { } 

Hebrew aleph 
Aleph ... 
Transfinite cardinal 
_{1}
+ _{0}
= _{1} 
º 
Degree symbol 
... degree(s) 
Angular measure 
= 45º 

Greek theta 
... theta ... 
Angular variable 
= 90º 

Greek phi 
... phi ... 
Angular variable 
= 45º 

Greek lambda 
... lambda ... 
wavelength 
= 70 cm 
µ 
Greek mu 
micro (10^{6}) 
prefix multiplier 
C = 0.001 µF 

Greek pi 
... pi ... 
General science 
3.14159 

Greek omega 
... omega ... 
Volume of an object 
R_{2} = 330 

Greek omega 
... omega ... 
Transfinite ordinal 
= 36,000
rad/s 
, N 
Enhanced or bold N 
The set of natural
numbers 
Number theory 
= {0, 1,
2, 3, ...} 
, Z 
Enhanced or bold Z 
The set of integers 
Number theory 
= {0, 1,
1, 2, 2, 3, 3, ...} 
, Q 
Enhanced or bold Q 
The set of rational
numbers 
Number theory 
= {a/b
 a and b are in } 
, R 
Enhanced or bold R 
The set of real numbers 
Number theory 
What is the cardinality
of ? 