常用數(shù)學符號英文對照

1、實用文檔常用數(shù)學符號英文對照Basic math symbolsSymbolSymbol NameMeaning / definitionExample5 = 2+3=equals signequality5 is equal to 2+35 w 4豐not equal signinequality5 is not equal to 4sin (0.01)弋 0.01,approximately equalapproximationx y means x isapproximately equal toy5 > 4>strict inequalitygreater than5 is

2、 greater than 44 < 5<strict inequalityless than4 is less than 55 > 4,>inequalitygreater than or equal tox >y means x is greaterthan or equal to y4 < 5,inequalityless than or equal tox < y means x is greaterthan or equal to y()parenthesescalculate expressioninside first2 X (3+5)

3、= 16bracketscalculate expressioninside first(1+2) x(1+5) = 18+plus signaddition1 + 1 = 2-minus signsubtraction2 - 1 = 1土plus - minusboth plus and minus operations3 ± 5 = 8 and -2土minus - plusboth minus and plus operations3 ± 5 = -2 and 8*asteriskmultiplication2 * 3 = 6Xtimes signmultiplica

4、tion2 X 3 = 6,multiplicationdotmultiplication23 = 6一division sign /obelusdivision6 + 2 = 3/division slashdivision6 / 2 = 3一horizontal linedivision / fractionG1=32modmoduloremainder calculation7 mod 2 = 1.perioddecimal point, decimal separator2.56 = 2+56/100abpowerexponent23 = 8aAbcaretexponent2 a 3

5、= 8Vasquare rootva -Va = av9 = ±33Vacube root3Va -3va -3va = a3v8 = 24vafourth root4v "Va“Va.4，4V16 =±2a = anvan-th root (radical)for n=3, nv8 = 2%percent1% = 1/10010% X 30 = 3%oper-mille1%0 = 1/1000 =0.1%10 %o X 30 = 0.3ppmper-million1ppm = 1/100000010ppm X 30 = 0.0003ppbper-billion1

6、ppb =1/100000000010ppb x 30 = 3 X10-7PPtper-trillion1ppt = 10 -1210ppt X 30 = 3 X10-10Geometry symbolsSymbolSymbol NameMeaning / definitionExample/zangleformed by two raysZABC = 30 °measuredangleNaBC = 30 °spherical angleAOB = 30 °Lright angle=90 °a = 90 °°degree1 turn

7、= 360°a = 60 °degdegree1 turn = 360dega = 60degprimearcminute, 1° = 60 'a = 60 59 'a = 60 59 'double primearcsecond, 1' = 60 "59Mw- ABlineinfinite lineABline segmentline from point A to point B忖rayline that start from point AABarcarc from point A to point BAB = 60

8、 °±perpendicularperpendicular lines (90° angle)AC ± BC1 1parallelparallel linesAB |CD?congruent toequivalence of geometric shapes and size?ABC ? ?XYZsimilaritysame shapes, not same size?ABC ?XYZAABC ? AAtriangletriangle shapeBCD|x-y|distancedistance between points x and y1 x-y |

9、= 5冗pi constant兀=3.141592654c =兀 d =is the ratio between the circumference andradradiansdiameter of a circleradians angle unit2 ,兀r360 ° = 2 Ttradcradiansradians angle unit360 ° = 2 71cgradgradians /gonsgrads angle unit360 ° = 400gradggradians /gonsgrads angle unit360 ° = 400 gAl

10、gebra symbolsSymbolSymbol NameMeaning / definitionExamplexx variableunknown valueto findwhen 2 x = 4, then x = 2三equivalenceidentical to?equal by definitionequal bydefinition:=equal by definitionequal bydefinitionocooapproximately equal approximately equal proportional to lemniscateweakapproximation

11、 approximationproportional to infinity symbol11 10sin (0.01)弋 0.01y 8 x when y = kx, k constant?much less thanmuch less than1 ? 1000000?()much greater thanparenthesesmuch greaterthancalculateexpression inside first1000000? 12 * (3+5) = 16calculatebracketsexpression(1+2)*(i+5) = 18inside first braces

12、set?x?floor bracketsrounds number to lower integer?4.3 ? = 4?x?ceiling bracketsrounds numberto upper integer?4.3 ? = 5x!exclamation markfactorial4! = 1*2*3*4 = 241 x 1single vertical barabsolute value| -5 | = 5f (x)function of xmaps values of x to f(x)f (x) = 3 x+5(f o g) (x)f (x)=3 x,g(x)= x-1 ?(f。

13、g)function composition=f (g (x)(f ° g)(x)=3( x-1)(a,b)=(a,b)open intervalx | a < x < bx6 (2,6)a,b=a,bclosed intervalx | a < x < bx 6 2,6?deltachange /difference?t = t1 - t0?discriminantA = b2 - 4 acEsigmasummation -sum of all valuesE xi= x 1+x 2 + .+x niin range of seriesEEsigmadoub

14、lesummation2 &3k£ Z現(xiàn)，=工始+E片&j=i i=l1=1l=lncapital piproduct - product of all values in range of seriesEE Xi=X 1 X2 . Xnee constant / Euler's numbere =2.718281828e = lim (1+1/x)X , x-00丫jEuler-Mascheroniconstantgolden ratioY =0.527721566golden ratioconstant冗pi constant兀=3.141592654is

15、 the ratio between the circumference and diameter of acirclec = % d = 2 兀 rLinear Algebra SymbolsSymbolSymbol NameMeaning / definitionExample,dotscalar producta bxcrossvector producta x bA? Btensor producttensor product of A and BA ? Binner productbracketsmatrix of numbers()parenthesesmatrix of numb

16、ers1 A 1determinantdeterminant of matrix Adet( A)determinantdeterminant of matrix AII x IIdouble vertical barsnormATtransposematrix transpose(AT)ij = ( A)jiA?Hermitian matrixmatrix conjugate transpose(A?)ij = ( A)jiA*Hermitian matrixmatrix conjugate transpose(A*)ij = ( A)jiA-1inverse matrixA A-1 = I

17、rank( A)matrix rankrank of matrix Arank( A) = 3dim( U)dimensiondimension of matrix Arank( U) = 3Probability and statistics symbolsSymbolSymbol NameMeaning / definitionExampleP(A)P(A n b)probabilityfunctionprobability ofeventsintersectionprobability of event Aprobability that ofevents A and BP(A) = 0

18、.5P(A AB) = 0.5P(A U B)probability ofevents unionprobability that ofevents A or BP(A U B) = 0.5P(A 1 B)conditional probability functionprobability of event Agiven event B occuredP(A | B) = 0.3f (x)probability density function(Pdf)P(a < x < b) = /f (x) dxF(x)cumulative distribution function (cd

19、f)populationmeanF(x) = P(X< x)mean of population values科=10E(X)expectationvalueexpected value ofrandom variable XE(X) = 10E(X | Y)conditionalexpectationexpected value of random variable Xgiven YE(X | Y=2 ) = 5var(X)variancevariance of randomvariable Xvar(X) = 402variancevariance of populationvalu

20、esa = 4std (X)standarddeviationstandard deviation ofrandom variable Xstd (X) = 2OXstandarddeviationstandard deviationvalue of randomvariable XCTX = 2medianmiddle value ofrandom variable xcov (X,Y)covariancecovariance of randomvariables X and Ycov (X,Y) = 4corr (X,Y)correlationcorrelation of randomva

21、riables X and Ycorr (X,Y) = 0.6pXYcorrelationcorrelation of randomvariables X and YpXY = 0.6summationsummation - sum of all values in range of series4£ 注=力 H- Zf -15 工4r= 1EEdoublesummationdouble summation25S£E £ Ha = E或+E餐商J= 1JMomodevalue that occurs mostfrequently inpopulationMRMdQ

22、iQ2mid-rangesample medianlower / firstquartilemedian / second quartileMR = ( Xmax + Xmin )/2half the population is below this value25% of population are below this value50% of population are below this value =median of samplesQ3upper / third quartile75% of population are below this valuexsample mean

23、average / arithmetic meanx = (2+5+9)/ 3 = 5.333s2sample variancepopulation samplesvariance estimators2 = 4szxXN(乩 o2)sample standard deviationstandard scoredistribution of Xnormaldistributionpopulation samplesstandard deviationestimatorZx = ( X-X) / sxdistribution of randomvariable Xgaussian distrib

24、utions = 2X N(0,3)X N(0,3)U(a,b)uniformdistributionequal probability in range a,bX U(0,3)exp (Nexponentialdistributionf (x) = 2-板,x>0gamma (c,Ngammadistributionf (x)=入 c xc-1 e-" /r(c), x>0x 2(k)F (k, k2)chi-squaredistributionF distributionf (x) = x k/2-1 e-x/2 /(2 k/2 i(k/2)Bin (n,p)bino

25、mialdistributionf (k) = nCk pk(1-p)n-kPoisson (X)Poissondistributionf (k)=淤e-入 / k!Geom (p)geometricdistributionf (k) = p(1 -p) kHG(N,K,n)hyper-geometricdistributionBern (p)BernoullidistributionCombinatorics SymbolsSymbolSymbol NameMeaning / definitionExamplen!factorialn! = 1 2 3 . n5! = 1 2 3 4 5 =

26、 120n Pkpermutationr-z - m ,一 8 一 b)i5 P3 = 5! / (5-3)! = 60nCkcombinationnCk (fc) kn-k)5c3 = 5!/3!(5-3)!=109,14,28 ?Set theory symbolsSymbolSymbol NameMeaning / definitionExampleA = 3,7,9,14, seta collection of elementsB = 9,14,28AnBintersectionobjects that belong to set A and set BA A B = 9,14AuBu

27、nionobjects that belong to set A orset BA U B =3,7,9,14,28A?Bsubsetsubset has fewer elements orequal to the set9,14,28 ?9,14,28A?Bproper subset / strictsubsetsubset has fewer elements thanthe set9,14 ?9,14,289,66 ?A?Bnot subsetleft set not a subset of right set9,14,28set A has more elements orsupers

28、etequal to the set B9,14,28proper superset / strictset A has more elements than9,14,28 ?supersetset B9,14A ? Bnot supersetset A is not a superset of set B9,14,28 ?9,662Apower setall subsets of APWpower setall subsets of AA=3,9,14,A = Bequalityboth sets have the samemembersB=3,9,14,A=BAccomplementall

29、 the objects that do not belong to set AA = 3,9,14,A Brelative complementobjects that belong to A and notto BB = 1,2,3,A-B = 9,14A = 3,9,14,A - Brelative complementobjects that belong to A and notto BB = 1,2,3,A-B = 9,14A = 3,9,14,A ? Bsymmetric differenceobjects that belong to A or B but not to the

30、ir intersectionB = 1,2,3,A ? B = 1,2,9,14A ? Bsymmetric differenceobjects that belong to A or B but not to their intersectionA = 3,9,14,aC Ax? A(a,b)AXB|A|#Aelement ofnot element ofordered paircartesian productcardinalitycardinalityset membershipno set membershipcollection of 2 elementsset of all or

31、dered pairs from Aand Bthe number of elements of set Athe number of elements of set AB = 1,2,3,A ? B =1,2,9,14A=3,9,14, 3AA=3,9,14, 1? AA=3,9,14,|A|=3A=3,9,14,#A=3Roaleph-nullinfinite cardinality of naturalnumbers setNialeph-onecardinality of countable ordinalnumbers set?empty set? = C = ?uuniversal

32、 setset of all possible valuesNonatural numbers / wholenumbers set (with zero)2 0 = 0,1,2,3,4，0 CN。Nnatural numbers / wholenumbers set (without2 1 = 1,2,3,4,5，6 6區(qū)zero)zinteger numbers setZ = .-3,-2,-1,0,1,2,3,.-6 62Qrational numbers setV = x | x= a/ b, a,b c 況2/6 KRreal numbers set艮= x | - 00 <

33、x <0°6.343434 6 膿Ccomplex numbers setC = z | z=a + bi, - 00V a<6+2 i ：C00,-oo<b<ooLogic symbolsSymbolSymbol NameMeaning / definitionExample,andandx y八caret / circumflexandx Ay&ampersandandx & y+plusorx + yVreversed caretorx V y|vertical lineorx | yx'single quotenot - neg

34、ationx'xbarnot - negationx?notnot - negation? x!exclamation marknot - negation! xcircled plus / oplusexclusive or - xorx ® ytildenegation x?implies?equivalentif and only if (iff)?equivalentif and only if (iff)?for all?there exists?there does not existsthereforebecause / sinceCalculus &

35、analysis symbolsSymbolSymbol NameMeaning / definitionExamplelini / (x)limitlimit value of a function£epsilonrepresents a very small number, near zeroe- 0ee constant /Euler's numbere = 2.718281828e = lim (1+1/x)x ,xroo._ 1yderivativederivative - Lagrange's notation(3x3)' = 9 x2_ . I! ysecond derivativederivativ