Mathematical Symbols
This table contains mathematical symbols and links to definitions of what they represent.
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Symbol  What it is  How it is read  How it is used  Sample expression 
+  Addition sign Logical OR symbol 
... plus ... ... or ... 
Sum of a few values Logical disjunction 
3 + 5 = 8 ¬(A + B) = ¬A * ¬B 
*  Multiplication sign Logical AND symbol 
... times ... ... and ... 
Product of two values Logical conjunction 
3 x 5 = 15 ¬(A * B) = ¬A + ¬B 
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 infinitely many values 

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 sign 
... minus ... Negative... 
Difference of two values, negative number 
3  5 = 2 
±  Plus/minus sign  ... plus or minus ...  Expression of range, error, or tolerance 
500 kbps ± 10% 
dot product sign  ... dot ...  Scalar (dot) product of two vectors 
A B = B A  
x  Cross product sign  ... cross ...  Vector (cross) product of two vectors 
A x B =  (B x A) 
Product sign  The product of ...  Product of three up to infinitely many values 

^  Carat  ... to the power of ...  exponent  2 ^ 5 = 32 
!  Exclamation  ... factorial  Product of all positive integers up to a certain value 
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 ... ... and so on indefinitely 
Extension of sequence  S = {1, 2, 3, ...} 
/  Slash  ... divided by ... ... over ... 
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, ratio sign 
... is to ... ... such that ... ... it is true that ... 
Division or ratio, symbol following logical quantifier or used in defining a set 
2:4 = 20:40 x : x > 4 and x < 5 x : x < 0 or x > 1 S = {x : x < 3} 
  Vertical line  ... such that ... ...it is true that ... 
Symbol following logical quantifier or used in defining a set 
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 ... increases without limit 
Infinite summations Infinite sequence Limit 
x : x <  
( )  Parentheses  ...quantity... ...list... ...set of coordinates... ...open interval 
Denotes a quantity, list, set of coordinates, or an open interval 
(x + y) + z (a_{1}, a_{2}, a_{3}, a_{4}) (x,y,z) (3,5) 
[ ]  Square brackets  ... the quantity ... ... the closed interval ... 
Denotes a quantity or a closed interval 
w + [(x + y) + z] [3,5] 
( ]  Hybrid brackets  ... the halfopen interval ...  Denotes a halfopen interval 
(3,5] 
[ )  Hybrid brackets  ... the halfopen interval ...  Denotes a halfopen interval 
[3,5) 
{ }  Curly brackets  ... the quantity ... ... the set ... 
Denotes a quantity or a set  E = {2, 4, 6, 8, ...} 
=  Equal sign  ... equals ...  Indicates two values are the same 
(5) = 5 2z^{2} + 4z  6 = 0 
proportionality sign  ... is proportional to ...  Indicates two variables change in direct proportion 
x y  
~  Similarity sign  ... is similar to ...  Indicates two objects are geometrically similar 
ABC ~ DEF 
Approximate equal sign 
... is approximately equal to ...  Indicates two values are close to each other 
x + y z  
Inequality sign  ... is not equal to ...  Indicates two values are different 
x y  
<  Inequality sign  ... is less than ...  Indicates value on left is smaller than value on right 
3 < 5 x < y 
Inequality sign  ... is less than or equal to ... ... is at most equal to ... 
Indicates value on left is smaller than or equal to value on right 
x y  
>  Inequality sign  ... is greater than ...  Indicates value on left is larger than value on right 
5 > 3 x > y 
Inequality sign  ... is greater than or equal to ...  Indicates value on left is larger than or equal to value on right 
x y  
   absolute value sign  The absolute value of ...  Distance of value from origin in number line, plane, or space 
 3  = 3 
increment sign, Triangle symbol 
the change in ... triangle ... 
Indicates a small change, Denotes vertices of triangle 
m = y / x ABC = DEF 

Perpendicularity symbol 
... is perpendicular to ...  Geometry  L M  
//  Parallel symbol  ... is parallel to ...  Geometry  L // M 
Angle symbol  Angle ...  Geometry  ABC = DEF  
Existential quantifier  For some ... There exists a(n) ... 
Logical statements  x : x > 4 and x < 5  
Universal quantifier  For all ... For every ... 
Logical statements  x : x < 0 or x > 1  
¬  Logical negation symbol 
not ...  Logical statements  ¬(¬A) A 
logical implication symbol 
... implies ... If ... then ... 
Logical statements  A B  
logical equivalence symbol 
... is logically equivalent to ... ... if and only if .. 
Logical statements  A B  
Three dots  ... therefore ... ... it follows that ... 
Logical statements or mathematical proofs 
x = y and y = z x = z 

Elementof symbol 
... is an element of a set ... 
Sets  a A  
Notelementof symbol 
... is not an element of a set ... 
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 ... ... intersected with ... 
Sets  A B = B A  
Null symbol  The null set The empty set 
Sets  = { }  
Hebrew aleph (uppercase) 
Aleph ...  Transfinite cardinal  _{1} + _{0} = _{1}  
º  Degree symbol  ... degree(s)  Angular measure Temperature 
= 45º T = +20 ºC 
Greek theta (lowercase) 
... theta ...  Angular variable  = 90º  
Greek phi (lowercase) 
... phi ...  Angular variable  = 45º  
Greek lambda (lowercase) 
... lambda ...  Wavelength Ratio Eigenvalue Lebesgue measure 
= 70 cm = 3:1 

µ  Greek mu (lowercase) 
micro (10^{6})  Prefix multiplier  C = 0.001 µF 
Greek pi (lowercase) 
... pi ...  General science  3.14159  
Greek omega (uppercase) 
... omega ...  Volume of an object Ohms (resistance) 
R_{2} = 330  
Greek omega (lowercase) 
... omega ...  Transfinite ordinal Angular velocity Period 
= 36,000 rad/s = 1/60 s 

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