数学符号大全

大数据 Alan 6年前 (2015-03-20) 4969次浏览 0个评论 扫描二维码

最近想要了解一下有关大数据、数据挖掘方面的知识,强烈发现数学知识都还给中学老师了。本来学理科的,可是大学里愣是被“文科化”了,看到那些数学符号连名称都记不起来了,所以分别在百度和谷歌上搜了下相关的信息,放在这里以供查看。

PEMDAS规则(运算符优先级):parentheses first, exponentiation second, multiplication/division third, and addition/subtraction fourth

1 几何符号

⊥   ∥   ∠   ⌒   ⊙   ≡   ≌     △

2 代数符号

∝   ∧   ∨   ~   ∫   ≠     ≤   ≥   ≈   ∞   ∶

3运算符号

×   ÷   √     ±

4集合符号

∪   ∩   ∈

5特殊符号

∑     π(圆周率)

6推理符号

|a|     ⊥     ∽     △     ∠     ∩     ∪     ≠     ≡     ±     ≥     ≤     ∈     ←

↑     →     ↓     ↖     ↗     ↘     ↙     ∥     ∧     ∨

&;   §

①   ②   ③   ④   ⑤   ⑥   ⑦   ⑧   ⑨   ⑩

Γ     Δ     Θ     Λ     Ξ     Ο     Π     Σ     Φ     Χ     Ψ     Ω

α     β     γ     δ     ε     ζ     η     θ     ι     κ     λ     μ     ν

ξ     ο     π     ρ     σ     τ     υ     φ     χ     ψ     ω

Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅸ Ⅹ Ⅺ Ⅻ

ⅰ ⅱ ⅲ ⅳ ⅴ ⅵ ⅶ ⅷ ⅸ ⅹ

∈   ∏   ∑   ∕   √   ∝   ∞   ∟ ∠     ∣   ∥   ∧   ∨   ∩   ∪   ∫   ∮

∴   ∵   ∶   ∷   ∽   ≈   ≌   ≒   ≠   ≡   ≤   ≥   ≦   ≧     ≮   ≯   ?   ⊙     ⊥

⊿   ⌒     ℃

指数0123:º¹²³

符号                 意义

∞                   无穷大

PI                   圆周率

|x|                   函数的绝对值

∪                   集合并

∩                   集合交

≥                   大于等于

≤                   小于等于

≡                   恒等于或同余

ln(x)                 自然对数

lg(x)                 以2为底的对数

log(x)               常用对数

floor(x)             上取整函数

ceil(x)               下取整函数

x mod y               求余数

{x}                   小数部分 x – floor(x)

∫f(x)δx             不定积分

∫[a:b]f(x)δx       a到b的定积分

[P]                   P为真等于1否则等于0

∑[1≤k≤n]f(k)   对n进行求和,可以拓广至很多情况

如:∑[n is prime][n < 10]f(n)

∑∑[1≤i≤j≤n]n^2

lim f(x) (x->?)       求极限

f(z)               f关于z的m阶导函数

C(n:m)               组合数,n中取m

P(n:m)               排列数

m|n                   m整除n

m⊥n                 m与n互质

a ∈ A               a属于集合A

#A                   集合A中的元素个数

 

 

SymbolSymbol NameMeaning / definitionExample
=equals signequality5 = 2+3
not equal signinequality5 ≠ 4
>strict inequalitygreater than5 > 4
<strict inequalityless than4 < 5
inequalitygreater than or equal to5 ≥ 4
inequalityless than or equal to4 ≤ 5
( )parenthesescalculate expression inside first2 × (3+5) = 16
[ ]bracketscalculate expression inside first[(1+2)*(1+5)] = 18
+plus signaddition1 + 1 = 2
minus signsubtraction2 − 1 = 1
±plus – minusboth plus and minus operations3 ± 5 = 8 and -2
minus – plusboth minus and plus operations3 ∓ 5 = -2 and 8
*asteriskmultiplication2 * 3 = 6
×times signmultiplication2 × 3 = 6
multiplication dotmultiplication2 ∙ 3 = 6
÷division sign / obelusdivision6 ÷ 2 = 3
/division slashdivision6 / 2 = 3
horizontal linedivision / fraction
modmoduloremainder calculation7 mod 2 = 1
.perioddecimal point, decimal separator2.56 = 2+56/100
abpowerexponent23 = 8
a^bcaretexponent2 ^ 3 = 8
asquare roota · a  = a√9 = ±3
3acube root 3a · 3√a  · 3√a  = a 3√8 = 2
4afourth root 4a · 4√a  · 4√a  · 4√a  = a 4√16 = ±2
nan-th root (radical)for n=3, n√8 = 2
%percent1% = 1/10010% × 30 = 3
per-mille1‰ = 1/1000 = 0.1%10‰ × 30 = 0.3
ppmper-million1ppm = 1/100000010ppm × 30 = 0.0003
ppbper-billion1ppb = 1/100000000010ppb × 30 = 3×10-7
pptper-trillion1ppt = 10-1210ppt × 30 = 3×10-10

Geometry symbols

SymbolSymbol NameMeaning / definitionExample
angleformed by two rays∠ABC = 30º
measured angleABC = 30º
spherical angleAOB = 30º
right angle= 90ºα = 90º
ºdegree1 turn = 360ºα = 60º
´arcminute1º = 60´α = 60º59′
´´arcsecond1´ = 60´´α = 60º59’59”
lineinfinite line
ABline segmentline from point A to point B
rayline that start from point A
arcarc from point A to point B= 60º
|perpendicularperpendicular lines (90º angle)AC | BC
||parallelparallel linesAB || CD
congruent toequivalence of geometric shapes and size∆ABC ≅ ∆XYZ
~similaritysame shapes, not same size∆ABC ~ ∆XYZ
Δtriangletriangle shapeΔABC ≅ ΔBCD
|xy|distancedistance between points x and y| xy | = 5
πpi constantπ = 3.141592654…is the ratio between the circumference and diameter of a circlec = π·d = 2·π·r
radradiansradians angle unit360º = 2π rad
gradgradsgrads angle unit360º = 400 grad

Algebra symbols

SymbolSymbol NameMeaning / definitionExample
xx variableunknown value to findwhen 2x = 4, then x = 2
equivalenceidentical to
equal by definitionequal by definition
:=equal by definitionequal by definition
~approximately equalweak approximation11 ~ 10
approximately equalapproximationsin(0.01) ≈ 0.01
proportional toproportional tof(x) ∝ g(x)
lemniscateinfinity symbol
much less thanmuch less than1 ≪ 1000000
much greater thanmuch greater than1000000 ≫ 1
( )parenthesescalculate expression inside first2 * (3+5) = 16
[ ]bracketscalculate expression inside first[(1+2)*(1+5)] = 18
{ }bracesset
xfloor bracketsrounds number to lower integer⌊4.3⌋= 4
xceiling bracketsrounds number to upper integer⌈4.3⌉= 5
x!exclamation markfactorial4! = 1*2*3*4 = 24
| x |single vertical barabsolute value| -5 | = 5
f (x)function of xmaps values of x to f(x)f (x) = 3x+5
(f g)function composition(f g) (x) = f (g(x))f (x)=3x, g(x)=x-1 ⇒(f g)(x)=3(x-1)
(a,b)open interval(a,b) = {x | a < x < b}x ∈ (2,6)
[a,b]closed interval[a,b] = {x | axb}x ∈ [2,6]
deltachange / differencet = t1 t0
discriminantΔ = b2 – 4ac
sigmasummation – sum of all values in range of series xi= x1+x2+…+xn
∑∑sigmadouble summation
capital piproduct – product of all values in range of series xi=x1∙x2∙…∙xn
ee constant / Euler’s numbere = 2.718281828…e = lim (1+1/x)x , x→∞
γEuler-Mascheroni  constantγ = 0.527721566…
φgolden ratiogolden ratio constant
πpi constantπ = 3.141592654…is the ratio between the circumference and diameter of a circlec = π·d = 2·π·r

Linear Algebra Symbols

SymbolSymbol NameMeaning / definitionExample
dotscalar producta b
×crossvector producta × b
ABtensor producttensor product of A and BAB
inner product
[ ]bracketsmatrix of numbers
( )parenthesesmatrix of numbers
| A |determinantdeterminant of matrix A
det(A)determinantdeterminant of matrix A
|| x ||double vertical barsnorm
A Ttransposematrix transpose(AT)ij = (A)ji
AHermitian matrixmatrix conjugate transpose(A)ij = (A)ji
A *Hermitian matrixmatrix conjugate transpose(A*)ij = (A)ji
A -1inverse matrixA A-1 = I
rank(A)matrix rankrank of matrix Arank(A) = 3
dim(U)dimensiondimension of matrix Arank(U) = 3

Probability and statistics symbols

SymbolSymbol NameMeaning / definitionExample
P(A)probability functionprobability of event AP(A) = 0.5
P(AB)probability of events intersectionprobability that of events A and BP(AB) = 0.5
P(AB)probability of events unionprobability that of events A or BP(AB) = 0.5
P(A | B)conditional probability functionprobability of event A given event B occuredP(A | B) = 0.3
f (x)probability density function (pdf)P(a x b) = ∫ f (x) dx
F(x)cumulative distribution function (cdf)F(x) = P(X x)
μpopulation meanmean of population valuesμ = 10
E(X)expectation valueexpected value of random variable XE(X) = 10
E(X | Y)conditional expectationexpected value of random variable X given YE(X | Y=2) = 5
var(X)variancevariance of random variable Xvar(X) = 4
σ2variancevariance of population valuesσ2 = 4
std(X)standard deviationstandard deviation of random variable Xstd(X) = 2
σXstandard deviationstandard deviation value of random variable XσX  = 2
medianmiddle value of random variable x
cov(X,Y)covariancecovariance of random variables X and Ycov(X,Y) = 4
corr(X,Y)correlationcorrelation of random variables X and Ycorr(X,Y) = 0.6
ρX,Ycorrelationcorrelation of random variables X and YρX,Y = 0.6
summationsummation – sum of all values in range of series
∑∑double summationdouble summation
Momodevalue that occurs most frequently in population
MRmid-rangeMR = (xmax+xmin)/2
Mdsample medianhalf the population is below this value
Q1lower / first quartile25% of population are below this value
Q2median / second quartile50% of population are below this value = median of samples
Q3upper / third quartile75% of population are below this value
xsample meanaverage / arithmetic mean x = (2+5+9) / 3 = 5.333
s 2sample variancepopulation samples variance estimators 2 = 4
ssample standard deviationpopulation samples standard deviation estimators = 2
zxstandard scorezx = (xx) / sx
X ~distribution of Xdistribution of random variable XX ~ N(0,3)
N(μ,σ2)normal distributiongaussian distributionX ~ N(0,3)
U(a,b)uniform distributionequal probability in range a,bX ~ U(0,3)
exp(λ)exponential distributionf (x) = λeλx , x≥0
gamma(c, λ)gamma distributionf (x) = λ c xc-1eλx / Γ(c), x≥0
χ 2(k)chi-square distributionf (x) = xk/2-1ex/2 / ( 2k/2 Γ(k/2) )
F (k1, k2)F distribution
Bin(n,p)binomial distributionf (k) = nCk pk(1-p)n-k
Poisson(λ)Poisson distributionf (k) = λkeλ / k!
Geom(p)geometric distributionf (k) =  p (1-p) k
HG(N,K,n)hyper-geometric distribution
Bern(p)Bernoulli distribution

Combinatorics Symbols

SymbolSymbol NameMeaning / definitionExample
n!factorialn! = 1·2·3·…·n5! = 1·2·3·4·5 = 120
nPkpermutation5P3 = 5! / (5-3)! = 60
nCkcombination5C3 = 5!/[3!(5-3)!]=10

Set theory symbols

SymbolSymbol NameMeaning / definitionExample
{ }seta collection of elementsA = {3,7,9,14},
B = {9,14,28}
A ∩ Bintersectionobjects that belong to set A and set BA ∩ B = {9,14}
A ∪ Bunionobjects that belong to set A or set BA ∪ B = {3,7,9,14,28}
A ⊆ Bsubsetsubset has fewer elements or equal to the set{9,14,28} ⊆ {9,14,28}
A ⊂ Bproper subset / strict subsetsubset has fewer elements than the set{9,14} ⊂ {9,14,28}
A ⊄ Bnot subsetleft set not a subset of right set{9,66} ⊄ {9,14,28}
A ⊇ Bsupersetset A has more elements or equal to the set B{9,14,28} ⊇ {9,14,28}
A ⊃ Bproper superset / strict supersetset A has more elements than set B{9,14,28} ⊃ {9,14}
A ⊅ Bnot supersetset A is not a superset of set B{9,14,28} ⊅ {9,66}
2Apower setall subsets of A
power setall subsets of A
A = Bequalityboth sets have the same membersA={3,9,14},
B={3,9,14},
A=B
Accomplementall the objects that do not belong to set A
A \ Brelative complementobjects that belong to A and not to BA = {3,9,14},
B = {1,2,3},
A-B = {9,14}
A – Brelative complementobjects that belong to A and not to BA = {3,9,14},
B = {1,2,3},
A-B = {9,14}
A ∆ Bsymmetric differenceobjects that belong to A or B but not to their intersectionA = {3,9,14},
B = {1,2,3},
A ∆ B = {1,2,9,14}
A ⊖ Bsymmetric differenceobjects that belong to A or B but not to their intersectionA = {3,9,14},
B = {1,2,3},
A ⊖ B = {1,2,9,14}
a∈Aelement ofset membership A={3,9,14}, 3 ∈ A
x∉Anot element ofno set membershipA={3,9,14}, 1 ∉ A
(a,b)ordered paircollection of 2 elements
A×Bcartesian productset of all ordered pairs from A and B
|A|cardinalitythe number of elements of set AA={3,9,14}, |A|=3
#Acardinalitythe number of elements of set AA={3,9,14}, #A=3
aleph-nullinfinite cardinality of natural numbers set
aleph-onecardinality of countable ordinal numbers set
Øempty setØ = { }C = {Ø}
universal setset of all possible values
0natural numbers / whole numbers  set (with zero)0 = {0,1,2,3,4,…}0 ∈ 0
1natural numbers / whole numbers  set (without zero)1 = {1,2,3,4,5,…}6 ∈ 1
integer numbers set= {…-3,-2,-1,0,1,2,3,…}-6 ∈
rational numbers set= {x | x=a/b, a,b∈}2/6 ∈
real numbers set= {x | -∞ < x <∞}6.343434 ∈
complex numbers set= {z | z=a+bi, -∞<a<∞,      -∞<b<∞}6+2i

Logic symbols

SymbolSymbol NameMeaning / definitionExample
·andandx · y
^caret / circumflexandx ^ y
&ampersandandx & y
+plusorx + y
reversed caretorxy
|vertical lineorx | y
xsingle quotenot – negationx
xbarnot – negation x
¬notnot – negation¬ x
!exclamation marknot – negation! x
circled plus / oplusexclusive or – xorxy
~tildenegation~ x
implies
equivalentif and only if (iff)
equivalentif and only if (iff)
for all
there exists
there does not exists
therefore
because / since

Calculus & analysis symbols

SymbolSymbol NameMeaning / definitionExample
limitlimit value of a function
εepsilonrepresents a very small number, near zeroε → 0
ee constant / Euler’s numbere = 2.718281828…e = lim (1+1/x)x , x→∞
y derivativederivative – Lagrange’s notation(3x3)’ = 9x2
y second derivativederivative of derivative(3x3)” = 18x
y(n)nth derivativen times derivation(3x3)(3) = 18
derivativederivative – Leibniz’s notationd(3x3)/dx = 9x2
second derivativederivative of derivatived2(3x3)/dx2 = 18x
nth derivativen times derivation
time derivativederivative by time – Newton’s notation
time second derivativederivative of derivative
Dx yderivativederivative – Euler’s notation
Dx2 ysecond derivativederivative of derivative
partial derivative∂(x2+y2)/∂x = 2x
integralopposite to derivation
double integralintegration of function of 2 variables
triple integralintegration of function of 3 variables
closed contour / line integral
closed surface integral
closed volume integral
[a,b]closed interval[a,b] = {x | a x b}
(a,b)open interval(a,b) = {x | a < x < b}
iimaginary uniti ≡ √-1z = 3 + 2i
z*complex conjugatez = a+biz*=abiz* = 3 + 2i
zcomplex conjugatez = a+biz = abiz = 3 + 2i
nabla / delgradient / divergence operatorf (x,y,z)
vector
unit vector
x * yconvolutiony(t) = x(t) * h(t)
Laplace transformF(s) = {f (t)}
Fourier transformX(ω) = {f (t)}
δdelta function
lemniscateinfinity symbol

Numeral symbols

NameEuropeanRomanHindu ArabicHebrew
zero0٠
one1I١א
two2II٢ב
three3III٣ג
four4IV٤ד
five5V٥ה
six6VI٦ו
seven7VII٧ז
eight8VIII٨ח
nine9IX٩ט
ten10X١٠י
eleven11XI١١יא
twelve12XII١٢יב
thirteen13XIII١٣יג
fourteen14XIV١٤יד
fifteen15XV١٥טו
sixteen16XVI١٦טז
seventeen17XVII١٧יז
eighteen18XVIII١٨יח
nineteen19XIX١٩יט
twenty20XX٢٠כ
thirty30XXX٣٠ל
fourty40XL٤٠מ
fifty50L٥٠נ
sixty60LX٦٠ס
seventy70LXX٧٠ע
eighty80LXXX٨٠פ
ninety90XC٩٠צ
one hundred100C١٠٠ק

 

Greek alphabet letters

Greek SymbolGreek Letter NameEnglish EquivalentPronunciation
Upper CaseLower Case
ΑαAlphaaal-fa
ΒβBetabbe-ta
ΓγGammagga-ma
ΔδDeltaddel-ta
ΕεEpsiloneep-si-lon
ΖζZetazze-ta
ΗηEtaheh-ta
ΘθThetathte-ta
ΙιIotaiio-ta
ΚκKappakka-pa
ΛλLambdallam-da
ΜμMumm-yoo
ΝνNunnoo
ΞξXixx-ee
ΟοOmicronoo-mee-c-ron
ΠπPippa-yee
ΡρRhorrow
ΣσSigmassig-ma
ΤτTautta-oo
ΥυUpsilonuoo-psi-lon
ΦφPhiphf-ee
ΧχChichkh-ee
ΨψPsipsp-see
ΩωOmegaoo-me-ga

Roman numerals

NumberRoman numeral
0not defined
1I
2II
3III
4IV
5V
6VI
7VII
8VIII
9IX
10X
11XI
12XII
13XIII
14XIV
15XV
16XVI
17XVII
18XVIII
19XIX
20XX
30XXX
40XL
50L
60LX
70LXX
80LXXX
90XC
100C
200CC
300CCC
400CD
500D
600DC
700DCC
800DCCC
900CM
1000M
5000V
10000X
50000L
100000C
500000D
1000000M
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