常用数学符号英文对照
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常用数学符号英文对照
Basic
math symbols
Symbol
Symbol
Name
Meaning / definition
Example
=
≠
≈
equals sign
equality
5 = 2+3
5 is equal to 2+3
5
≠
4
5 is not equal to 4
not
equal sign
inequality
approximately
equal
approximation
sin
(0.01)
≈
0.01,
x
≈
y
means
x
is
approximately equal to
y
5 > 4
5 is greater than 4
4 < 5
4 is less than 5
5
≥
4,
>
<
strict inequality
greater than
strict
inequality
less than
≥
inequality
greater than or equal to
x
≥
y
means
x
is greater
than or equal to
y
4
≤
5,
≤
inequality
less than or
equal to
x
≤
y
means
x
is greater
than or equal to
y
2
×
(3+5) = 16
( )
parentheses
[ ]
brackets
+
−
±
±
plus sign
calculate expression
inside
first
calculate expression
inside first
[(1+2)
×
(1+5)] =
18
addition
1 + 1 = 2
2
−
1 = 1
3
±
5 = 8 and -2
minus sign
subtraction
both plus and minus
operations
both minus and
plus
operations
plus - minus
minus - plus
3
±
5 = -2 and 8
。
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*
×
·
÷
/
–
asterisk
multiplication
2 * 3 = 6
2
×
3 = 6
2
·
3 = 6
times sign
multiplication
dot
division sign /
obelus
multiplication
multiplication
division
6
÷
2 = 3
division slash
division
6 / 2 = 3
horizontal line
division / fraction
remainder calculation
decimal point, decimal
separator
mod
modulo
7 mod 2 = 1
2.56 = 2+56/100
.
period
a
b
power
exponent
2
= 8
3
a^b
caret
√
a
3
exponent
2 ^
3
= 8
square root
√
a
·
√
a
=
a
√
9
=
±
3
√
a
cube root
√
a
fourth root
√
a
(radical)
%
percent
n-th root
3
√
a
·
√
a
·
√
a
= a
3
3
3
√
8
= 2
4
4
√
a
·
4
√
a
·
4
√
a
·
4
√
a
= a
4
√
16
=
±
2
n
for
n
=3,
n
√
8
= 2
1% = 1/100
1
‰
= 1/1000 =
0.1%
1ppm = 1/1000000
1ppb =
1/1000000000
1ppt = 10
-12
10%
×
30 = 3
10
‰
×
30 = 0.3
10ppm
×
30 = 0.0003
10ppb
×
30 =
3
×
10
10ppt
×
30 =
3
×
10
-10
-7
‰
per-mille
ppm
per-million
ppb
per-billion
ppt
per-trillion
Geometry
symbols
。
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Symbol
Symbol Name
Meaning /
definition
Example
∠
angle
formed by two rays
∠
ABC =
30
°
measured
angle
spherical
ABC = 30
°
angle
right
angle
degree
degree
prime
double prime
AOB =
30
°
α
= 90
°
α
=
60
°
α
= 60deg
α
=
60
°
59
′
α
= 60
°
59
′
59
″
∟
°
deg
= 90
°
1 turn = 360
°
1 turn = 360deg
arcminute,
1
°
=
60
′
arcsecond,
1
′
=
60
″
′
″
AB
line
infinite line
line segment
line from point
A to point B
⊥
| |
≅
~
Δ
ray
line that start from point A
arc
arc from point A to point B
= 60
°
AC
⊥
BC
perpendicular
perpendicular lines
(90
°
angle)
parallel
parallel lines
AB
| |
CD
congruent to
equivalence of geometric shapes and
size
∆
ABC
≅
∆
XYZ
similarity
same shapes, not same size
∆
ABC~
∆
XYZ
Δ
ABC
≅
Δ
BCD
|
x
-
y
| = 5
triangle
triangle shape
|
x
-
y
|
distance
distance between
points x and y
π
= 3.141592654...
π
pi constant
is the ratio between the circumference
and
diameter of a circle
c
=
π
·
d
=
2
·
π<
/p>
·
r
。
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rad
c
radians
radians
radians angle unit
radians
angle unit
360
°
=
2
π
rad
360
°
=
2
π
360
°
= 400
grad
360
°
=
400
g
c
grad
gradians
/
gons
grads angle unit
g
gradians
/
gons
grads
angle unit
Algebra symbols
Symbol
Symbol Name
Meaning /
definition
unknown value to
find
identical to
equal by
definition
equal by
definition
weak
approximation
approximation
Example
x
≡
≜
:=
~
≈
∝
∞
≪
≫
( )
x variable
when 2
x
= 4, then
x
= 2
equivalence
11 ~ 10
equal by definition
equal by definition
approximately equal
approximately equal
sin
(0.01)
≈
0.01
y
∝
x
when
y
=
kx, k
constant
proportional to
proportional
to
lemniscate
infinity
symbol
much
less than
much less than
1
≪
1000000
much
greater than
much
greater
than
1000000
≫
1
calculate
parentheses
expression
inside first
calculate
2 * (3+5) = 16
[ ]
{ }
brackets
expression
inside first
[(1+2)*(1+5)] = 18
braces
set
。
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⌊
x
⌋
⌈
x
⌉
floor brackets
rounds number
to
lower integer
rounds
number to
upper integer
⌊
4.3
⌋
= 4
ceiling brackets
⌈
4.3
⌉
= 5
x
!
exclamation mark
factorial
4! = 1*2*3*4 = 24
|
x
|
single vertical bar
absolute value
| -5 | = 5
f
(
x
)
function of x
maps values of
x
to f(x)
f
(
x
) =
3
x
+5
f
(
x
)=3
x
,
g
(
x
)=
x
-1
⇒
(
f
∘
g
)(<
/p>
x
)=3(
x
-
1)
x
∈
(2,6)
(
f
∘
g
)
function composition
(
f
∘
g
)
(
x
)
=
f
(
g
(
x
))
(
a
,
b
) =
{
x
|
a
<
x
<
b
} <
/p>
[
a
,
b
] =
{
x
|
a
≤
x
≤
b
}
change /
difference
< br>(
a
,
b
)
open interval
[
a
,
b
]
closed interval
∆
∆
∑
delta
x
∈
[2,6]
∆
t
=
t
-
t
1
0
discriminant
Δ
=
b
-
4
ac
summation -
sum
2
sigma
of all values in
∑
x
i
= x
1
+x
2
+...+x
< br>n
range of series
∑∑
sigma
double summation
product
- product
∏
capital pi
of all values in
∏
x
i
=x
1
∙
x
2
∙
...
∙
x
n
range
of series
e
γ
φ
π
e
constant
/
Euler's
number
e
=
2.718281828...
γ
=
0.527721566...
golden
ratio
constant
e
= lim (1+1/
x
)
x
,
x
→∞
Euler-Mascheroni
constant
golden
ratio
π
=
pi
constant
3.141592654...
c
=
π
·
d
= 2
·
π
·
r
is the ratio
。
5
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between the
circumference and
diameter
of a
circle
Linear Algebra Symbols
Symbol
Symbol Name
Meaning / definition
Example
·
×
dot
scalar product
a
·
b
a
×
b
A
⊗
B
cross
vector product
A
⊗
B
[ ]
( )
|
A
|
tensor product
tensor product of A and B
inner product
brackets
matrix of numbers
parentheses
matrix of numbers
determinant
determinant of matrix A
det(
A
)
determinant
||
x
||
double vertical bars
determinant of matrix A
norm
A
T
transpose
matrix
transpose
(
A
)
ij
=
(
A
)
ji
(
A
†
)
ij
=
(
A
)
ji
(
A
)
ij<
/p>
=
(
A
)
ji
*
T
A
†
A
*
Hermitian matrix
matrix conjugate transpose
Hermitian matrix
matrix
conjugate transpose
A
-1
inverse matrix
A A
-1
=
I
rank of matrix A
rank(
A
)
matrix rank
rank(
A
) = 3
。
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dim(
U
)
dimension
dimension of
matrix A
rank(
U
)
= 3
Probability and statistics symbols
Symbol
Symbol Name
probability
function
probability of
Meaning /
definition
probability of event
A
Example
P
(
A
)
P
(
A
∩
B
)
P
(
A
) =
0.5
events
intersection
probability that of
events A
and B
P
(
A
< br>∩
B
) = 0.5
P
(
A
∪
B
)
events union
conditional
probability of
probability
that of
events A or B
probability of event
A given
event B
occured
P
(
A
∪
B
)
= 0.5
P
(
A
|
B
)
probability
function
probability
P
(
A |
B
) = 0.3
f
(
x
)
density
function (pdf)
cumulative
P
(
a
≤
x
≤
b
)
=
∫
f
(
x
)
dx
F
(
x
)
μ
distribution
function (cdf)
F
(
x
)
=
P
(
X<
/p>
≤
x
)
population mean
mean of population
values
expected value of
random
variable X
expected value of
random variable X
given Y
variance of random
variable
X
variance of
population
values
standard
deviation
of
random variable X
μ
= 10
E
(
X
)
expectation
value
E
(
X
) =
10
E
(
X |
Y
)
expectation
var
(
X
)
σ
2
variance
conditional
E
(
X |
Y=2
) = 5
var
(
X
)
= 4
variance
σ
2
= 4
std
(
X
)
standard
deviation
std
(
X
)
= 2
。
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σ
X
standard
deviation
standard deviation
value of
random
variable X
middle
value of
random variable x
covariance of random
variables X and Y
correlation
of
random
variables X and Y
correlation
of
random
variables X and Y
summation
-
sum
of
all
σ
X
=
2
median
cov
(
X
,
Y
< br>)
covariance
cov
(
X,Y
) = 4
corr<
/p>
(
X
,
Y
)
correlation
ρ
X
,
Y
∑
correlation
corr
(
X,Y
)
= 0.6
ρ
X
Y
= 0.6
,
summation
values in range of
series
∑∑
double
summation
double summation
value that occurs
Mo
MR
Md
Q
1
mode
most frequently in
population
mid-range
MR
= (
x
max
+
x
min
)/2
half the population
is below
this value
25%
of
population
are
below this value
50%
of
population
are
below this value =
median of
samples
75%
of
population
are
below this value
average /
arithmetic
mean
population
samples
variance estimator
sample median
lower / first
quartile
Q
2
median / second
quartile
Q
3
upper / third
quartile
x
s
2
sample mean
x
= (2+5+9) / 3 =
5.333
sample variance
s
2
= 4
。
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