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.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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