数学符号英语念读.doc

Mathematics Symbols and Their English Explanations1/2a half or one half1/3a third or one third2/3two third1/4a quarter or one quarter; a fourth or one fourth1/10a tenth or one tenth1/100a one hundredth1/1000a one thousandth1/1234one over a thousand two hundred and thirty-four3/4three fourths or three quarters4/5three fifths or four over five113/300one hundred and thirteen over three hundredtwo and a half two and seven over eight or two and seven eighththree and one eighthfour and a thirda one hundred twenty-five and three fourth quarters0.1(or .1)point one or zero point one or nought point one0.01(or .01)point 0 one or zero point zero one or naught point naught one0.25(or .25)naught point two five or point two five0.045decimal point naught four five2.35two point three five4.four point nine recurring3.03three point naught three two six , two six recurring45.67four five forty-five point six seven38.72three eight point seven two or thirty-eight decimal seven two0.001(or .001)0 point 0 0 one naught point naught naught one or zero pointzero zero one or point naught naught one+plus; positive_minus; negativeplus or minus(or.)multiplied by ; times(or/)divided by= is equal to ; equalsis identically equal to(or;=)is approximately equal to ; approximately equalsidentical withnot equal toorapproachesgreater thanmuch grater thanequal to or less thanequal to or greater than( )round brackets; parentheses square bracketsangular brackets bracesIntersectionUnionis a member of set is a subset ofsimilar to ; difference*denotes an operationis equivalent toImplies orempty setMaps intoThereforeBecause:ratio sign, divided by, is to:equals, as (proportion)varies asinfinitysquare root ofcube root ofparallel todegreesminutes”secondsanglelength of line from A to Bvector product of A and B; magnitude of A times magnitude of B times sine of the angle from A to B; AB sin scalar product of A to B ; magnitude of A times magnitude of B times cosine of the angle form A to B ;AB cos I or jimaginary or square root of -1 or the imaginary cube roots of 1pi ; the ratio of the circumference of a circle to its diameter, approx.3.14159e or the base of natural logarithms, approx.2.71828 the eccentricity of a conic sectionx!factorial of xlog x to the base n or log x to the base 10 (common logarithm) or log x to the base (natural logarithm or Naperian logarithm )M modulus of common logarithms e = 0.4343, (x = x 0.4343) 10 = 2.3026, (x = x 2.3026) x x.xto n factors, the nth power of x, x to the power n or the nth root of x,x to the power one over n thX a x approaches the limit a(the angle between the radius vector and the polar axis) the angle thetasigmathe product of the terms indicatedthe absolute value of x the mean value of x ; x barb primeb double prime ; b second primeb triple primeb sub oneb sub twob sub mx dot ,first derivative of x with respect to timex two dot , second derivative of x with respect to timeexp x=(e = naperian log base )(abbreviation for )b double prime sub mf or Ffunctionf(x);F(x);(x)function f(or ) of xy = f(x)y is a function of x( finite difference or increment) deltaor x(the increment of x) delta x(an increment of x considered as tending to zero )dee of x ; dee x ; differential of x or the differential coefficient of y with respect to xthe first derivative of y with respect to x/the second derivative of y with respect x;/the nth derivative of y with respect x/the partial derivative of y with respect u ,uwhere y is a function of u and another variable (or variables)(x)the first derivative of function F of x with respect to xi/+j/+k/ del ; nabla; vector differential operatornnth del (nabla)Laplacian operator 4!Factorial =1line integral around a closed path integralintegral between limits a and bvector Fx+yx plus y (a+b)bracket a plus b bracket closeda = ba equals b ; a is equal to b ; a is b a ba is not equal to b ; a is not baba plus or minus baba is approximately equal to baba is greater than baba is much far greater than baba is greater than or equal to ba is not greater than baba is less than baba is much less than baa is less than or equal to baa is not less than baa is perpendicular to bx=x approaches infinityaa is identically equal to b ; a is of identityangle aaba is parallel to babthe difference between a and baa varies directly as bone one is onetwice two is foursix time multiplied by five equals is equal to; are; makes ; make thirtythirty is five times as large as sixs=vts equals is equal to v multiplied by t; s equals v times t1:2the ratio of one to two 12 divided by 3 equals is 420:5=16:4the radio of 20 to 5 equals the ratio of 16 to 4 ; 20 is to 5 as 16 is to 4a:b : c:da is to b as c is to da+b=ca plus b is are; equals; is equal to cc-b=ac minus b is equals; is equal to a; b from c leaves av equals s divided by t; c is s over t7+37+312 is greater than 7 plus 372-16=5672 minus 16 is equals; is equal to 56; 16 from 72 leaves 56x square ; x squared; the square of x; the second power of x; x to the second power =25the second power of 5 is 25; 5 square is 25 ; 5 to the second power is equal to 25y cube ; y cubed ;the cube of y ; y to the third power ; y to the thirdy to the minus tenth(power)=the square root of 4 is equals plus or minus 2the cube root of athe fifth root of x square the square root of five hundred and eighteenthe cubic root of nine hundred and thirty3x=5three times x equals 5x raised to the third power divided by five equals y squaredx squared with y squared equals 10a equals v sub t minus v over divided by ta plus b minus c multiplied by d , all divided by e equals feight plus six and five-eighths minus three decimal point six eight multiplied by four, all divided by two and a half余1323 into 4567 goes 198 times, and 13 remainder45+70+152=26745, 70 and 152 added together are 267%percent2%two per centper mille5five per millethree eighths (of one) percent0.3%point three percenthalf tontow third of a tonthree quarters of a kilometer1.75kmone point seven five kilometersixty miles per hourtwenty degrees 6 minutes 6 feet 10 seconds 10 inches0zero degree Centigrade Celsius100one a hundred degrees centigrade32thirty-two degrees FahrenheitSet theory, relations, functionsX , YSetXx is a member of the set Xx is not a member of XSet A is contained in set XA is not contained in XUnion of sets X and YIntersection of sets X and Y+,+,Symmetric difference of setsUnion of all the sets XIntersection of all the sets XNull set , empty setComplement of the set XX-Y, XYDifference of sets X and YThe set of all x with the property p(x , y , z), ( x, y, z)Ordered set of elements x , y, and z; to be distinguished from (x, y, z), for example( x, y, z)Unordered set, the set whose elements are x, y, z, and no others , i=1,2.,n The set whose members are , where i is any whole number from 1 to n , i=1,2., The set whose members are , where i is any positive whole numberCartesian product, set of all (x , y) such that The set whose elements are a, where Xry ,R x , yRelationEquivalence relations, for example, congruence ,Transitive relations, for example, numerical orderFunction, mapping, transformationInverse mappingg。FComposite functions: (g。F) ( x )=g( f( x ) )f( X )Image of X by fInverse-image set, counter image1-1, one-oneRead “one-to-one correspondence”Diagram : the diagram is commutative in case f=g Partial mapping, restriction of function f to set AX , card X, Cardinal of the set A , dDenumerable infinityC , c ,2Power of continuumOrder type of the set of positive integersRead “countably ”Number, numerical functions1( 1 ) 20( 10 )100Read “ from 1 to 20 in intervals of 1, and from 20 to 100 in intervals of 10 ”Constconstanta0The number A is nonnegative, or, the matrix A is positive definite, or, the matrix A has nonnegative entriesxyRead “ x divides y ”xy mod pRead “ x congruent to y modulo p ”Continued fractionsarc sine of xSinhsinus hyperbolic, the hyperbolic sine a ,b Closed interval, a ,bHalf-open Interval ( open at the right )( a ,b),a ,bOpen intervala, ),a, Interval closed at the left, infinite to the rightSet of all real numbersmax f(x),max f(x) Maximum of f(x) when x is in the set XminMinimumsup , Supremum, least upper boundinf , g.1.bInfimum, greatest lower boundlim sup ,limit superiorlim inf ,imit inferiorl . i . m .limit in the meanComplex variablesZ , Complex conjugateRe, Real part Im,Imaginary partArgArgumentJacobian, functional determinantIntegral (for example , Lebesgue integral ) of function f over set E with respect to measure f(n)log n as nf(n)/log n approaches 1 as nf(n)=0(log n ) as nf(n)/log n is bounded as nf(n)=0(log n )f(n)/log n approaches zerof(x)b, f(x)bf(x) increases, approaching the limit bf(x)b, f(x)bf(x) decreases, approaching the limit ba . e . ,p . p.almost everywhereess supessential superemumspace of continuous functionthe class of functions having continuous kth derivative (on a, b )same as Lipchitz class of function,Lp , Lpa , bspace of functions having integrable absolute pth power ( on a, b )same as ( C ,a ), ( C , p )cesaro summablitySpecial functionxThe integral part of xBinomial coefficient n!/k!( n-k )!Legendre symbolExponential functionsinhx, coshx, tanhxHyperbolic functionssnx , cnx , dnxJacobi elliptic functions( x )Weierstrass elliptic function Gamma functionBessel functionCharacteristic function of the set X, X(x)=1 in case xX, otherwise X(x)=0sgn xSignum: sgn 0=0. while sgn x=x for x0Dirac delta functionAlgebra, tensors, operators+, . , law of composition in algebraic systemse , 0Identity, unit , neutral element ( of an additive system )e ,1, I,Identity, unit , neutral element ( of a general algebraic system ) e ,e ,E ,PidempotentInverse of aHom ( M,N )Group of all homomorphisms of M into NG/HFactor group, group of cosetsK : kDimension of K over k,+Direct sumTensor product, Kronecker productExterior product, Grassmann productVectorInner product, scalar product, dot productyOuter product, vector product, cross product,Norm of the vector xAx, xAThe image of x under the transformation AKronecker delta: Transpose of the matrix AAdjoint, Hermitian conjugate of ATr A ,S