一些英语表达式的读法
数学符号 1/2 1/3 2/3 1/4 1/1234 读法： A half 或 one half A third 或 one third Two thirds A quarter或 one quarter One over a thousand two hundred and thirty-four Two and a half Two and seven over eight O point one或 zero point one O point o one或 zero point zero one Sixty miles per hour Twenty degrees Zero degree Centigrade Six times (multiplied by)five equals (is equal to; are ; makes; make) thirty S equals (is equal to)v multiplied by t The ratio of one to two A plus B is(are;equals;is equal to)C C minus B is(equals;is equal to)A V equals s divided by t Three plus seven is less than 12 Twelve is greater than seven plus three x square;x squared;the square of x;the second power of x y cube;y cubed;the cube of y;y to the three power y to the minus tenth(power) The square root of 4 is(equals)plus or minus 2 The cube root of a The fifth root of x square The square root of five hundred and eighteen Two percent Infinity;indefinitely great Angle 1 272 820.1 0.01 60mi/hr 20 0℃ 6×5=30 S=vt 1:2 A+B=C C-B=A V=s/t 3+7<12 12>7+3 x2 y3 y10 4=2 3a X2 5518 2% AB AB Length of line from A to B Vecter product of A and B;magnitude of A times magnitude of B times since of the angle from A to B;ABsinAB AB Scalar product of A and B; magnitude of A times magnitude of B times cosine of the angle from A to B; AB cosAB ‖,∥ 3Perpendicular; is perpendicular to Parallel; is parallel to Square root of Cube root of nth root of Equivalent;similar Round branckets;parentheses Square [angular] brackets Braces Intersection,logical product Union,logical sum Is an element of;is member of set Is equivalent to implies Is not an element of a is approximately equal to b a is greater than b a is much less than b a is much greater than b a is not less than b a is perpendicular to b X approaches infinity a is identically equal to b; a is of identity to b p to the power x The absolute value of a;magnitude of a Factorial n Exponential(to the base e)of x logx to the base a; logarithm to the base a of x n～ ( ) [ ] ｛｝ ∩ ∪ ∈ ab a＞b a＜＜b a＞＞b a≮b ab X=∞ ab p ︱a ︳ n! exp x xlogax lnx a‖b Sin χ Cosx Tanx,tgx Cotx,ctgx Secx Cosecx,cscx Arcsin x Arccosx Arctanx,arctan x Arccotx,arcctgx Arccosecx,arccscx Imz ‖z‖ logx to the base e;natural logarithm of x a is parallel to b Sine of x Cosine of x Tangent of x Cotangent of x Secant of x Cosecant of x;1/sinx Arc sine of x Arc cosine of x Arc tangent of x Arc cotangent of x Arc cosecant of x Imaginary part of z Modulus of z Conjugate of z Increment of x; delta x Total differential of the function ƒ Derivative of the function ƒ with respect to χ nth derivative of the function ƒ An indefinite integral of the function ƒ or the set of indefinite integrals of the function ƒ Definiteintegral of the function ƒ from a to b x approaches the limit a b prime b double prime Sets x is a member of the set X x is not a member of X Set A is contained in X A is not contained in X Union of sets X and Y Intersection of sets X and Y Null set,empty set Complement of the set X Difference of sets X and Y Ordered set of elements x,y,and z,for example Cartesian product, set of all (x,y) such that xX,yY, Descartes z,z* △x,δx ｄƒ ｄƒ /ｄχ D ƒ dnfn Df,dxnf(x)dx baf(x)dxx→a b’ b’’ X,Y x∈X xX AX AX XY, X+Y XY, X·Y ,0 X’ , CX X-Y ,X\\Y (x,y,z) , XY {ai}iI R(x,y) ,,～ The set whose elements are ai,where i∈I Relation Equivalence relations ,for example ,congruence Transitive relations ,for example ,numerical order Function,mapping,transformation inverse mapping Composite functions(gf)(x)=g(f(x)) Image of X by ƒ Inverse-image set ,counter image One- to- one correspondence Partial mapping restriction of function ƒ to set A Cardinal of the set A One and four-tenths 1又10分之4 From 1 to 20 in intervals of 1从1到10间隔1和从20到100间隔10 Constant 常数 The number A is nonnegative ,or, the matrix A has nonnegative entires数A是非负数或矩阵A是正定的，或矩阵A之元皆非负 x divides y x除y x congrument to y modulo p x同余（全等）模p Continued fractions 连分数 Closed interval 闭区间 Half-open interval (open at the right) 半开区间（右开） Open interval 开区间 Interval closed at the left ,infinite to the right 左边闭右边无限的区间 Maximum of f(x)when x is in the set X 当x属于X集时，f(x)的最大值 ,＞,≧,>>,＜,≦ Y ƒ:XX,Xff1 gf ƒ (X) f1(x) 1-1,one_one ƒ|A CardX,X,{X} 1.4;14 1(1)20(10)100 Const A≧0 x|y xy mod p 11a0 a1a2[a,b] [a,b),[a,b[ (a,b) [a,),[a,) maxxXf(x),max{f(x)|xX} min Sup l.u.b Minimum 最小值 Supermum ,least upper bound 下确界,最小上界 Inf,g.l.b Infermum ,greatest lower bound 下确界,最大下界 B is the limit of f(x) as x approaches a 当x 趋于 a时f(x) 的极限值是b limxaf(x)b,limxaf(x)b, f(x)b,xa limxaf(x),limxa0f(x),f(a) limsup,lim Limit of f(x) as x approaches a from the left 当x 从左边趋于a 时f(x) 的极值 Limit superior 上极限 Limit inferior 下极限 Jacobian,functional determinant Jacobi行列式，函数行列式 Integral (for example,lebesgue integral) of function liminf,lim (u,v)D(u,v), (x,y)D(x,y)Ef(x)d(x) f over set E with respect to measure 在集E（对于测度）上函数f(x)的积分（例如，Lebesgue积分） f(n)～logn,当 n f(n)/logn approaches 1 as n 当 n时，f(n)/logn趋于1 f(n)0(logn)，当n f(n)/logn is bounded as n 当n时，f(n)/logn是有界的 f(x)↗b, f(x)↑b f(x) increases ,approaching the limit b f(x)减少，趋于极限b a.e.,p.p Ess sup Almost everywhere 几乎处处 Essential supermum 殆上确界 Space of continuous functions连续函数空间 The class of function having continuous kth derivative (on[a,b])有连续的k阶导数（在a,b的闭区间）的函数类 Space of functions having integrable absolute pth power (on[a,b]) 绝对p次幂（在[a,b]上是可积的函数空间） The integral part of x x的整数部分 C0,C0(X),C(X) Ck,Ck[a,b] Lp,Lp,Lp[a,b] [x] n ksinhx,coshx,tanhx snx,cnx,dnx (x) Binomial coefficient ,n!/k!(n-k)! 二项式系数 Hyperbolic functions双曲函数 Jacobi elliptic functions Jacobi 椭圆函数 Gamma function 函数 Bessel function Bessel函数 Characteristic function of the set X:x(x) =1 in case x∈X,ortherwise J(x) Xx(x) x(x)=0 集X 的特征函1,xX数：x(x)= 0,xX(x) e,0 E,1,I Dirac delta function Dirac 函数 Identity,unit,neutral element(of a general algebraic system) 恒等，可逆元素，零元素（加法系的） Identity ,unit,neutral,element(of a general algebraic system) 恒等，可逆元素，零元素(一般代数系的) Idempotent 幂等元 Inverse of a a 的倒数 Group of all homomorphisms of M into N M到N的所有同态组 Factor group ,group of cosets商群，傍系群 Dimension of K over k ， k上K的维数 Direct sum 直合 Tensor product ,Kronecker product张量积，Kronecker积 Exterior product ,Grassmann product,外积，Grassmann积 Vector 向量 Inner product,scalar product,dot product内积，纯量积，点积 Outer product ,vector product,cross product外积，向e,E,P a1 Hom(M,N) G/H [K：k] , ∧ x,X， （x,y） x·y，X·Y，X×Y, x∧y, 量积，叉积 |x|, ||x||, Norm of the vector x 向量x的模方 The image of x under the transformation A x在A变换下的象 Transpose of the matrix A 矩阵A转置 Adjoint ,hermitian conjugate of A伴随阵，A的Hermite共轭 Trace of the matrix A 矩阵A的迹 Determinant of the matrix A Finite differences有限差分 Divided differences均差 Gradient of f f的梯度 Divergence of v v的散度 Curl of 的旋度 Laplacian Laplace算子 Full orthogonal group全正交群 Special orthogonal group特殊正交群 Sentences,prepositional functions,propositions语句，命题函数，命题 Negation ,read”not p”否定，读作“不是p” Disjunction,read”p or q”,”p,q”or both析取，“p或q” Conjunction,read”p and q”合取，读“p和q” Implication,read “p implies q ”or “if p then q”蕴涵。读“p蕴涵q”或’’如果p然后q” Equivalence,read”p is equivalent to q”or ”p if and only if q～”等价，读“p等价q”或“p当且仅当q” Parentheses 括号 Universal quantifier,read”for all”or “for every”全称量词，读“对于全部”或“对于每一个” Existential quantifier,read”there is a”or “there exists”存在量词，读“有一”或“存在” Truth ,falsity(values)真，假（值） Identity 恒等式 Definititional identity 定义恒等 Ax,xA A',tA,At,tA A* TrA,SpA DetA,|A| f(x) [x0,x1],[x0,x1,x2] f,gradf ·,div n,curl,rot 2,,divgrad GL（n,R） SO(n,R),O+(n,R) p,q,P(x), -p,～p,non p,Np, p∨q,p+q,Apq p∧q,p>q,p&q,Kpq pq,pq,pq,Cpq pq,pq,pq,Epq,p iff q （），[ ]，{ }，--- ，∑， , 0，1 DF,df, En Enclidean n space n维Euclid空间 n sphere n维球面 Metric ,distance between points p and q度量，p,q之间的距离 Frontier,boundary of X X的边界 Interior of X X的内部 Union of countably many closed sets可数多个闭集的并 Intersection of countably many open sets可数多个开集的并 Random variables 随机变量 Probability that X≦2, X≦2的概率 Conditional probability 条件概率 Expectation of X X的数学期望 Conditional expectation 条件数学期望 Cumulative distribution function累积分布函数 Probability density function 概率密度函数 Characteristic function特征函数 Standard deviance标准偏差 Variance 方差 Sn (p,q),d(p,q) FrX,frX,X Int X, F G X,Y P(X≦2),Pr(X≦2) P(X≦2|Y≧1) E(X) E(X|Y≧1) c.d.f. p.d.f. e.f. ,s.d. 2,var
