Sutra: International Journal of Mathematical Science Education,
Vol. 2, No. 1, 2009
32
Useful 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
2+6=8
¬(A + B) = ¬A * ¬B
*
Multiplication sign
Logical AND symbol
... times ...
... and ...
Product of two
values
Logical
conjunction
2 x 6 = 12
¬(A * B) = ¬A + ¬B
x
Multiplication sign
... times ...
Product of two
values
4x2=8
·
Multiplication sign
... times ...
Product of two
values
4·2=8
summation sign
The summation of
...
Sum of many or
infinitely many
values
Integral sign
The integral of ...
integration
double integral
sign
The double integral
of ...
integration
Triple integral sign
The triple integral
of ...
integration
Line integral sign
The line integral of
...
integration
Surface integral sign
The surface
integral of ...
integration
-
Subtraction sign
Minus sign
... minus ...
Negative...
Difference of two
values,
negative number
2 - 6 = -4
±
Plus/minus sign
... plus or minus ...
Expression of
range,
error, or tolerance
540 kbps ± 10%
Dot product sign
... dot ...
Scalar (dot)
product
of two vectors
A B= B A
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
x
^
2
3
x dx = x /3
+c
f(x,y) dx dy
f(x,y,z) dx dy
dz
F dx
F(x,y,z) dx dy
2 ^ 4 = 16
Sutra: International Journal of Mathematical Science Education,
Vol. 2, No. 1, 2009
33
Exclamation
... factoriall
Product of all
positive
integers up to a
certain value
surd
... root of ...
Algebraic
expressions
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
... is to ...
... such that ...
... it is true that ...
Division or ratio ,
symbol following
logical quantifier
or
used in defining a
set
!
3! = 6
z=
(x + y)
4 = ±2
2:4 = 20:40
:
Colon,
ratio sign
∃x : x > 4 and x < 5
∀x : x < 0 or x > -1
S = {x : x < 3}
|
::
Vertical line
Double colon
... such that ...
...it is true that ...
Symbol following
logical quantifier
or
used in defining a
set
... averaged with ... arithmetic mean
∃x | x > 4 and x < 5
∀x | x < 0 or x > -1
S = {x | x < 3}
3 :: 11 = 7
lemniscate
... infinity
... increases
without limit
Infinite
summations
Infinite sequence
Limit
( )
Parentheses
...quantity...
...list...
...set of
coordinates...
...open interval
Denotes a
quantity, list,
set of
coordinates, or
an
open interval
(x + y) + z
(a1, a 2, 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]
[2,4]
( ]
Hybrid brackets
... the half-open
interval ...
Denotes a
half-open interval
(2,4]
[ )
Hybrid brackets
... the half-open
interval ...
Denotes a
half-open interval
[2,4)
{ }
Curly brackets
... the quantity ...
... the set ...
Denotes a
quantity or a set
E = {2, 4, 6, 8, ...}
∀x : x <
34
Sutra: International Journal of Mathematical Science Education,
Vol. 2, No. 1, 2009
=
~
<
>
Equal sign
... equals ...
Indicates two
values
are the same
Proportionality sign
... is proportional to
...
Indicates two
variables
change in direct
proportion
Similarity sign
... is similar to ...
Indicates two
objects are
geometrically
similar
Approximate
equal sign
... is approximately
equal to ...
Indicates two
values are
close to each
other
Inequality sign
... is not equal to ...
Indicates two
values
are different
Inequality sign
... is less than ...
Indicates value
on left
is smaller than
value on right
2<4
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
4>1
x>y
... is greater than
or equal to ...
Indicates value
on left
is larger than or
equal to
value on right
x y
The absolute value
of ...
Distance of value
from
origin in number
line,
plane, or space
| -5 | = 5
Triangle symbol
the change in ...
triangle ...
Indicates a small
change,
Denotes vertices
of triangle
Perpendicularity
symbol
... is perpendicular
to ...
Geometry
L
Parallel symbol
... is parallel to ...
Geometry
L // M
angle symbol
Angle ...
Geometry
Existential quantifier
For some ...
There exists a(n) ...
Logical
statements
Universal quantifier
For all ...
For every ...
Logical
statements
Inequality sign
| |
absolute value sign
increment sign,
//
-(-6) = 6
2
2z + 4z - 6 = 0
x
y
ABC ~ DEF
x+y
z
x
y
m= y/ x
ABC = DEF
∠ABC =
M
∠DEF
∃x : x > 4 and x < 5
∀x : x < 0 or x > -1
Sutra: International Journal of Mathematical Science Education,
Vol. 2, No. 1, 2009
¬
Logical negation
symbol
not ...
Logical
statements
¬(¬A)
... implies ...
If ... then ...
Logical
statements
A
B
... is logically
equivalent to ...
... if and only if ..
Logical
statements
A
B
... therefore ...
... it follows that ...
Logical
statements or
mathematical
proofs
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
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
logical implication
symbol
logical
equivalence
symbol
Three dots
º
35
A
x = y and y = z
x=z
={}
1
+
0
=
1
wavelength
µ
Ratio
Eigenvalue
Lebesgue
measure
Greek lambda
(lowercase)
... lambda ...
= 70 cm
= 3:1
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)
Greek omega
(lowercase)
... omega ...
Transfinite ordinal
Angular velocity
Period
R2 = 330
= 36,000 rad/s
= 1/60 s
36
Sutra: International Journal of Mathematical Science Education,
Vol. 2, No. 1, 2009
,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 ?