常用数学符号英文对照.docx
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常用数学符号英文对照
常用数学符号英文对照
Basicmathsymbols
Symbol
SymbolName
Meaning/definition
Example
=
equalssign
equality
5=2+3
5isequalto2+3
≠
notequalsign
inequality
5≠4
5isnotequalto4
≈
approximatelyequal
approximation
sin（0.01）≈0.01,
x ≈ y means x isapproximatelyequalto y
>
strictinequality
greaterthan
5>4
5isgreaterthan4
<
strictinequality
lessthan
4<5
4islessthan5
≥
inequality
greaterthanorequalto
5≥4,
x ≥ y means x isgreaterthanorequalto y
≤
inequality
lessthanorequalto
4≤5,
x≤y means x isgreaterthanorequalto y
（）
parentheses
calculateexpressioninsidefirst
2×（3+5）=16
[]
brackets
calculateexpressioninsidefirst
[（1+2）×（1+5）]=18
+
plussign
addition
1+1=2
−
minussign
subtraction
2−1=1
±
plus-minus
bothplusandminusoperations
3±5=8and-2
±
minus-plus
bothminusandplusoperations
3±5=-2and8
*
asterisk
multiplication
2*3=6
×
timessign
multiplication
2×3=6
·
multiplicationdot
multiplication
2·3=6
÷
divisionsign/obelus
division
6÷2=3
/
divisionslash
division
6/2=3
–
horizontalline
division/fraction
mod
modulo
remaindercalculation
7mod2=1
.
period
decimalpoint,decimalseparator
2.56=2+56/100
ab
power
exponent
23 =8
a^b
caret
exponent
2^3 =8
√a
squareroot
√a · √a =a
√9 =±3
3√a
cuberoot
3√a · 3√a · 3√a =a
3√8 =2
4√a
fourthroot
4√a · 4√a · 4√a · 4√a =a
4√16 =±2
n√a
n-throot（radical）
for n=3, n√8 =2
%
percent
1%=1/100
10%×30=3
‰
per-mille
1‰=1/1000=0.1%
10‰×30=0.3
ppm
per-million
1ppm=1/1000000
10ppm×30=0.0003
ppb
per-billion
1ppb=1/1000000000
10ppb×30=3×10-7
ppt
per-trillion
1ppt=10-12
10ppt×30=3×10-10
Geometrysymbols
Symbol
SymbolName
Meaning/definition
Example
∠
angle
formedbytworays
∠ABC=30°
measuredangle
ABC=30°
sphericalangle
AOB=30°
∟
rightangle
=90°
α=90°
°
degree
1turn=360°
α=60°
deg
degree
1turn=360deg
α=60deg
′
prime
arcminute,1°=60′
α=60°59′
″
doubleprime
arcsecond,1′=60″
α=60°59′59″
line
infiniteline
AB
linesegment
linefrompointAtopointB
ray
linethatstartfrompointA
arc
arcfrompointAtopointB
=60°
⊥
perpendicular
perpendicularlines（90°angle）
AC ⊥ BC
||
parallel
parallellines
AB || CD
≅
congruentto
equivalenceofgeometricshapesandsize
∆ABC≅∆XYZ
~
similarity
sameshapes,notsamesize
∆ABC~∆XYZ
Δ
triangle
triangleshape
ΔABC≅ΔBCD
|x-y|
distance
distancebetweenpointsxandy
| x-y |=5
π
piconstant
π =3.141592654...
istheratiobetweenthecircumferenceanddiameterofacircle
c = π·d =2·π·r
rad
radians
radiansangleunit
360°=2πrad
c
radians
radiansangleunit
360°=2π c
grad
gradians/gons
gradsangleunit
360°=400grad
g
gradians/gons
gradsangleunit
360°=400 g
Algebrasymbols
Symbol
SymbolName
Meaning/definition
Example
x
xvariable
unknownvaluetofind
when2x =4,then x =2
≡
equivalence
identicalto
≜
equalbydefinition
equalbydefinition
:
=
equalbydefinition
equalbydefinition
~
approximatelyequal
weakapproximation
11~10
≈
approximatelyequal
approximation
sin（0.01）≈0.01
∝
proportionalto
proportionalto
y ∝ x when y = kx,k constant
∞
lemniscate
infinitysymbol
≪
muchlessthan
muchlessthan
1≪1000000
≫
muchgreaterthan
muchgreaterthan
1000000≫1
（）
parentheses
calculateexpressioninsidefirst
2*（3+5）=16
[]
brackets
calculateexpressioninsidefirst
[（1+2）*（1+5）]=18
{}
braces
set
⌊x⌋
floorbrackets
roundsnumbertolowerinteger
⌊4.3⌋=4
⌈x⌉
ceilingbrackets
roundsnumbertoupperinteger
⌈4.3⌉=5
x!
exclamationmark
factorial
4!
=1*2*3*4=24
| x |
singleverticalbar
absolutevalue
|-5|=5
f （x）
functionofx
mapsvaluesofxtof（x）
f （x）=3x+5
（f ∘ g）
functioncomposition
（f ∘ g）（x）= f （g（x））
f （x）=3x,g（x）=x-1⇒（f ∘ g）（x）=3（x-1）
（a,b）
openinterval
（a,b）={x | a < x < b}
x∈（2,6）
[a,b]
closedinterval
[a,b]={x | a ≤ x ≤ b}
x ∈[2,6]
∆
delta
change/difference
∆t = t1 - t0
∆
discriminant
Δ= b2 -4ac
∑
sigma
summation-sumofallvaluesinrangeofseries
∑ xi=x1+x2+...+xn
∑∑
sigma
doublesummation
∏
capitalpi
product-productofallvaluesinrangeofseries
∏ xi=x1∙x2∙...∙xn
e
econstant /Euler'snumber
e =2.718281828...
e =lim（1+1/x）x , x→∞
γ
Euler-Mascheroni constant
γ=0.527721566...
φ
goldenratio
goldenratioconstant
π
piconstant
π =3.141592654...
istheratiobetweenthecircumferenceanddiameterofacircle
c = π·d =2·π·r
LinearAlgebraSymbols
Symbol
SymbolName
Meaning/definition
Example
·
dot
scalarproduct
a · b
×
cross
vectorproduct
a × b
A⊗B
tensorproduct
tensorproductofAandB
A ⊗ B
innerproduct
[]
brackets
matrixofnumbers
（）
parentheses
matrixofnumbers
| A |
determinant
determinantofmatrixA
det（A）
determinant
determinantofmatrixA
|| x ||
doubleverticalbars
norm
AT
transpose
matrixtranspose
（AT）ij =（A）ji
A†
Hermitianmatrix
matrixconjugatetranspose
（A†）ij =（A）ji
A*
Hermitianmatrix
matrixconjugatetranspose
（A*）ij =（A）ji
A -1
inversematrix
AA-1 = I
rank（A）
matrixrank
rankofmatrixA
rank（A）=3
dim（U）
dimension
dimensionofmatrixA
rank（U）=3
Probabilityandstatisticssymbols
Symbol
SymbolName
Meaning/definition
Example
P（A）
probabilityfunction
probabilityofeventA
P（A）=0.5
P（A ∩ B）
probabilityofeventsintersection
probabilitythatofeventsAandB
P（A∩B）=0.5
P（A ∪B）
probabilityofeventsunion
probabilitythatofeventsAorB
P（A∪B）=0.5
P（A | B）
conditionalprobabilityfunction
probabilityofeventAgiveneventBoccured
P（A|B）=0.3
f （x）
probabilitydensityfunction（pdf）
P（a ≤ x ≤ b）= ∫f （x） dx
F（x）
cumulativedistributionfunction（cdf）
F（x）= P（X≤ x）
μ
populationmean
meanofpopulationvalues
μ =10
E（X）
expectationvalue
expectedvalueofrandomvariableX
E（X）=10
E（X|Y）
conditionalexpectation
expectedvalueofrandomvariableXgivenY
E（X|Y=2）=5
var（X）
variance
varianceofrandomvariableX
var（X）=4
σ2
variance
varianceofpopulationvalues
σ2 =4
std（X）
standarddeviation
standarddeviationofrandomvariableX
std（X）=2
σX
standarddeviation
standarddeviationvalueofrandomvariableX
σX = 2
median
middlevalueofrandomvariablex
cov（X,Y）
covariance
covarianceofrandomvariablesXandY
cov（X,Y）=4
corr（X,Y）
correlation
correlationofrandomvariablesXandY
corr（X,Y）=0.6
ρX,Y
correlation
correlationofrandomvariablesXandY
ρX,Y =0.6
∑
summation
summation-sumofallvaluesinrangeofseries
∑∑
doublesummation
doublesummation
Mo
mode
valuethatoccursmostfrequentlyinpopulation
MR
mid-range
MR =（xmax+xmin）/2
Md
samplemedian
halfthepopulationisbelowthisvalue
Q1
lower/firstquartile
25%ofpopulationarebelowthisvalue
Q2
median/secondquartile
50%ofpopulationarebelowthisvalue=medianofsamples
Q3
upper/thirdquartile
75%ofpopulationarebelowthisvalue
x
samplemean
average/arithmeticmean
x =（2+5+9）/3=5.333
s 2
samplevariance
populationsamplesvarianceestimator
s 2 =4
s
samplestandarddeviation
populationsamplesstandarddeviationestimator
s =2
zx
standardscore
zx =（x-x）/ sx
X ~
distribution ofX
distributionofrandomvariableX
X ~ N（0,3）
N（μ,σ2）
normaldistribution
gaussiandistribution
X ~ N（0,3）
U（a,b）
uniformdistribution
equalprobabilityinrangea,b
X ~ U（0,3）
exp（λ）
exponentialdistribution
f （x） =λe-λx , x≥0
gamma（c,λ）
gammadistribution
f （x） =λcxc-1e-λx /Γ（c）, x≥0
χ 2（k）
chi-squaredistribution
f （x） =xk/2-1e-x/2 /（2k/2 Γ（k/2））
F （k1,k2）
Fdistribution
Bin（n,p）
binomialdistribution
f （k） = nCk pk（1-p）n-k
Poisson（λ）
Poissondistribution
f （k） =λke-λ / k!
Geom（p）
geometricdistribution
f （k） = p（1-p） k
HG（N,K,n）
hyper-geometricdistribution
Bern（p）
Bernoullidistribution
CombinatoricsSymbols
Symbol
SymbolName
Meaning/definition
Example
n!
factorial
n!
=1·2·3·...·n
5!
=1·2·3·4·5=120
nPk
permutation
5P3 = 5!
/（5-3）!
=60
nCk
combination
5C3 = 5!
/[3!
（5-3）!
]=10
Settheorysymbols
Symbol
SymbolName
Meaning/definition
Example
{}
set
acollectionofelements
A={3,7,9,14},
B={9,14,28}
A∩B
intersection
objectsthatbelongtosetAandsetB
A∩B={9,14}
A∪B
union
objectsthatbelongtosetAorsetB
A∪B={3,7,9,14,28}
A⊆B
subset
subsethasfewerelementsorequaltotheset
{9,14,28}⊆{9,14,28}
A⊂B
propersubset/strictsubset
subsethasfewerelementsthantheset
{9,14}⊂{9,14,28}
A⊄B
notsubset
leftsetnotasubsetofrightset
{9,66}⊄{9,14,28}
A⊇B
superset
setAhasmoreelementsorequaltothesetB
{9,14,28}⊇{9,14,28}
A⊃B
propersuperset/strictsuperset
setAhasmoreelementsthansetB
{9,14,28}⊃{9,14}
A⊅B
notsuperset
setAisnotasupersetofsetB
{9,14,28}⊅{9,66}
2A
powerset
allsubsetsofA
powerset
allsubsetsofA
A=B
equality
bothsetshavethesamemembers
A={3,9,14},
B={3,9,14},
A=B
Ac
complement
alltheobjectsthatdonotbelongtosetA
A\B
relativecomplement
objectsthatbelongtoAandnottoB
A={3,9,14},
B={1,2,3},
A-B={9,14}
A-B
relativecomplement
objectsthatbelongtoAandnottoB
A={3,9,14},
B={1,2,3},
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