Mathematical Symbols

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

... factoriall

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

= 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)

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 ?