Useful Mathematical Symbols

32 Sutra: International Journal of Mathematical Science Education, Vol. 2, No. 1, 2009

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

4 x 2 = 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 The double integral

sign

of ...

integration

x2 dx = x3/3 + c

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

2 - 6 = -4

Expression of

?

Plus/minus sign ... plus or minus ...

range,

540 kbps ? 10%

error, or tolerance

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 ^ 4 = 16

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Product of all

!

Exclamation

... factoriall

positive integers up to a

certain value

3! = 6

surd

... root of ...

Algebraic expressions

z = (x + y)

square root symbol

The square root of ...

Algebraic expressions

4 = ?2

... and so on up to

...

Continuation sign

... ... and so on

Extension of sequence

indefinitely

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

2:4 = 20:40

Division or ratio ,

:

Colon, ratio sign

... is to ... ... such that ... ... it is true that ...

symbol following logical quantifier

or used in defining a

x : x > 4 and x < 5 x : x < 0 or x > -1

set

S = {x : x < 3}

Symbol following x | x > 4 and x < 5

|

Vertical line

... such that ... ...it is true that ...

logical quantifier or

used in defining a

x | x < 0 or x > -1

set

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] [2,4]

( ]

Hybrid brackets

... the half-open

Denotes a

interval ...

half-open interval

(2,4]

[ )

Hybrid brackets

... the half-open

Denotes a

interval ...

half-open interval

[2,4)

{ }

Curly brackets

... the quantity ...

Denotes a

... the set ...

quantity or a set E = {2, 4, 6, 8, ...}

34 Sutra: International Journal of Mathematical Science Education, Vol. 2, No. 1, 2009

=

Equal sign

... equals ...

Indicates two values

are the same

-(-6) = 6 2z2 + 4z - 6 = 0

Proportionality sign

... is proportional to ...

Indicates two variables

change in direct proportion

x y

Indicates two

~

Similarity sign

... is similar to ...

objects are geometrically

ABC ~ DEF

similar

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

Indicates value

<

Inequality sign

... is less than ...

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

Indicates value

>

Inequality sign

... is greater than ...

on left is larger than

value on right

4 > 1 x > y

Indicates value

Inequality sign

... is greater than or equal to ...

on left

is larger than or equal to

x y

value on right

Distance of value

| |

absolute value sign

The absolute value of ...

from origin in number

line,

plane, or space

| -5 | = 5

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

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?

Logical negation symbol

not ...

Logical statements

?(?A) A

logical implication symbol

logical equivalence

symbol

... implies ... If ... then ...

... is logically equivalent to ... ... if and only if ..

Three dots

... therefore ... ... it follows that ...

Element-of symbol

... is an element of a set ...

Logical statements

Logical statements

Logical statements or mathematical

proofs

Sets

A B A B

x = y and y = z x = z

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 Null symbol

... intersect ... ... intersected with

...

The null set The empty set

Sets Sets

A B=B A = { }

Hebrew aleph (uppercase)

Aleph ...

Transfinite cardinal

1+ 0= 1

?

Degree symbol

... degree(s)

Angular measure Temperature

= 45? T = +20 ?C

Greek theta (lowercase)

... theta ...

Angular variable

= 90?

Greek phi (lowercase)

Greek lambda (lowercase)

... phi ... ... lambda ...

Angular variable

wavelength Ratio

Eigenvalue Lebesgue measure

= 45?

= 70 cm = 3:1

?

Greek mu (lowercase)

micro- (10-6)

prefix multiplier

C = 0.001 ?F

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

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

, Z

Enhanced or bold Z The set of integers

Number theory Set theory

, Q

Enhanced or bold Q The set of rational numbers

Number theory Set theory

, R Enhanced or bold R

The set of real numbers

Number theory Set theory

= {0, 1, 2, 3, ...}

= {0, 1, -1, 2, -2, 3, -3, ...}

= {a/b | a and b are

in }

What is the cardinality of ?

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