Definition

Mathematical symbols

TechTarget Contributor
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This list of commonly used mathematical symbols explains what each math symbol is, how it is used and provides a sample expression. 

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 x2 dx = x3/3 + 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
(a1, a2, a3, a4)
(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 half-open interval ... Denotes a
half-open interval		 (3,5]
[  ) Hybrid brackets ... the half-open interval ... Denotes a
half-open 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
2z2 + 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
Element-of
symbol		 ... is an element of
a set ...		 Sets a A
Not-element-of
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		 T = +20 ºC
 θ Greek theta
(lowercase)		 ... theta ... Angular variable  θ = 90º
φ Greek phi
(lowercase)		 ... phi ... Angular variable = 45º
λ 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)		 R2 = 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 ?

This was last updated in June 2021

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