常用数学符号英文对照.docx

常用数学符号英文对照常用数学符号英文对照 Basic math symbols Symbol Symbol Name Meaning / definition Example = equals sign equality 5 = 2+3 5 is equal to 2+3 not equal sign inequality 5 4 5 is not equal to 4 approximately sin(0.01) 0.01, equal approximation x y means x is approximately equal to y > strict inequality greater than 5 > 4 5 is greater than 4 < strict inequality less than 4 < 5 4 is less than 5 5 4, inequality greater than or equal to x y means x is greater than or equal to y 4 5, inequality less than or equal to x y means x is greater than or equal to y ( ) parentheses calculate expression inside first 2 × (3+5) = 16 brackets calculate expression inside first (1+2)×(1+5) = 18 + plus sign addition 1 + 1 = 2 minus sign subtraction 2 1 = 1 ± plus - minus both plus and minus operations 3 ± 5 = 8 and -2 ± minus - plus both minus and plus operations 3 ± 5 = -2 and 8 * asterisk multiplication 2 * 3 = 6 1 × · ÷ / times sign multiplication dot division sign / obelus division slash multiplication multiplication 2 × 3 = 6 2 · 3 = 6 6 ÷ 2 = 3 6 / 2 = 3 division division horizontal line division / fraction remainder calculation decimal point, decimal separator exponent exponent mod modulo 7 mod 2 = 1 2.56 = 2+56/100 23 = 8 2 3 = 8 9 = ±3 3. ab ab a 34period power caret square root cube root fourth root a · a = a 3a a a a · 3a · 3a = a a · 4a · 4a · 4a = a 8 = 2 16 = ±2 44nn-th root (radical) percent per-mille for n=3, n8 = 2 10% × 30 = 3 10 × 30 = 0.3 10ppm × 30 = 0.0003 10ppb × 30 = 3×10-7 10ppt × 30 = 3×10-10 % ppb ppt 1% = 1/100 1 = 1/1000 = 0.1% 1ppm = 1/1000000 1ppb = 1/1000000000 1ppt = 10-12 ppm per-million per-billion per-trillion Geometry symbols Symbol Symbol Name Meaning / definition Example angle formed by two rays ABC = 30° measured angle ABC = 30° spherical angle right angle AOB = 30° = 90° = 90° 2 ° deg degree degree prime double prime 1 turn = 360° 1 turn = 360deg arcminute, 1° = 60 arcsecond, 1 = 60 = 60° = 60deg = 60°59 = 60°5959 AB line infinite line line segment line from point A to point B | | |x-y| rad cray line that start from point A arc arc from point A to point B = 60° AC BC AB | | CD ABC XYZ ABC XYZ ABC BCD | x-y | = 5 perpendicular perpendicular lines (90° angle) parallel parallel lines congruent to equivalence of geometric shapes and size similarity triangle distance same shapes, not same size triangle shape distance between points x and y = 3.141592654. pi constant is the ratio between the circumference and diameter of a circle c = ·d = 2··r radians radians radians angle unit radians angle unit 360° = 2 rad 360° = 2 c 360° = 400 grad 360° = 400 g grad gradians / gons grads angle unit g gradians / gons grads angle unit Algebra symbols Symbol Symbol Name Meaning / definition Example 3 x x variable unknown value to find when 2x = 4, then x = 2 equivalence identical to equal by definition equal by definition := equal by definition equal by definition approximately equal weak approximation 11 10 approximately equal approximation sin(0.01) 0.01 proportional to proportional to y x when y = kx, k constant lemniscate infinity symbol much less than much less than 1 1000000 much greater than much greater than 1000000 1 calculate ( ) parentheses expression 2 * (3+5) = 16 inside first calculate brackets expression (1+2)*(1+5) = 18 inside first braces set x floor brackets rounds number to lower integer 4.3 = 4 x ceiling brackets rounds number to upper integer 4.3 = 5 x! exclamation mark factorial 4! = 1*2*3*4 = 24 | x | single vertical bar absolute value | -5 | = 5 f (x) function of x maps 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 (2,6) 4 x | a < x < b a,b closed interval a,b = x | a x b change / difference x 2,6 delta discriminant t = t1 - t0 = b2 - 4ac summation - sigma sum of all values in range of series double summation product - xi= x1+x2+.+xn sigma capital pi product of all values in range of series xi=x1x2.xn e e constant / Euler's number e = 2.718281828. = 0.527721566. golden ratio constant e = lim (1+1/x)x , x Euler-Mascheroni constant golden ratio = 3.141592654. is the ratio pi constant between the circumference and diameter of a circle c = ·d = 2··r Linear Algebra Symbols Symbol Symbol Name dot cross Meaning / definition scalar product vector product Example · × a · b a × b 5 AB ( ) | A | det(A) | x | AT A A* A -1 tensor product tensor product of A and B A B inner product brackets parentheses determinant determinant double vertical bars transpose Hermitian matrix Hermitian matrix inverse matrix matrix of numbers matrix of numbers determinant of matrix A determinant of matrix A norm matrix transpose matrix conjugate transpose matrix conjugate transpose (AT)ij = (A)ji (A)ij = (A)ji (A*)ij = (A)ji A A-1 = I rank of matrix A dimension of matrix A rank(A) matrix rank dim(U) dimension rank(A) = 3 rank(U) = 3 Probability and statistics symbols Symbol Symbol Name probability function probability of Meaning / definition Example P(A) probability of event A P(A) = 0.5 P(A B) events intersection probability of probability that of events A and B P(AB) = 0.5 P(A B) events union conditional probability that of events A or B probability of event A given event B occured P(AB) = 0.5 P(A | B) probability function probability P(A | B) = 0.3 f (x) F(x) density function (pdf) cumulative P(a x b) = f (x) dx F(x) = P(X x) 6 distribution function (cdf) population mean of population mean values = 10 E(X) expectation expected value of value random variable X E(X) = 10 expected value of E(X | Y) conditional expectation random variable X E(X | Y=2) = 5 given Y var(X) variance variance of random variable X var(X) = 4 2variance variance of population values 2 = 4 std(X) standard standard deviation of deviation random variable X std(X) = 2 standard standard deviation X deviation value of random X = 2 variable X median middle value of random variable x covariance of cov(X,Y) covariance random variables X cov(X,Y) = 4 and Y correlation of corr(X,Y) correlation random variables X corr(X,Y) = 0.6 and Y correlation of X,Y correlation random variables X X,Y = 0.6 and Y summation - sum of summation all values in range of series double summation double summation 7 value that occurs Mo mode most frequently in population MR mid-range MR = (xmax+xmin)/2 Md sample median half the population is below this value Qlower / first 25% of population 1 quartile are below this value Qmedian / 50% of population 2 second quartile are below this value = median of samples Qupper / third 75% of population 3 quartile are below this value x sample mean average / arithmetic mean x = (2+5+9) / 3 = 5.333 ssample population samples 2 variance variance estimator s 2 = 4 sample population samples s standard standard deviation s = 2 deviation estimator zx standard score zx = (x-x) / sx X distribution of X distribution of random variable X X N(0,3) N(,2) normal distribution gaussian distribution X N(0,3) U(a,b) uniform equal probability in distribution range a,b X U(0,3) exp() exponential distribution f (x) = e-x , x0 gamma(c, ) gamma f (x) = c xc-1e-x / distribution (c), x0 2(k) chi-square f (x) = xk/2-1e-x/2 / distribution ( 2k/2 (k/2) ) F (k1, k2) F distribution 8 Bin(n,p) binomial distribution Poisson distribution geometric distribution hyper-geometric distribution Bernoulli distribution f (k) = nCk pk(1-p)n-k Poisson() f (k) = ke- / k! Geom(p) f (k) = p(1-p) k HG(N,K,n) Bern(p) Combinatorics Symbols Symbol Symbol Name Meaning / definition Example n! nPk nCk factorial n! = 1·2·3·.·n 5! = 1·2·3·4·5 = 120 5P3 = 5! / (5-3)! = 60 permutation combination 5C3 = 5!/3!(5-3)!=10 Set theory symbols Symbol Symbol Name Meaning / definition Example set a collection of elements A = 3,7,9,14, B = 9,14,28 A B = 9,14 A B = 3,7,9,14,28 9,14,28 9,14,28 9,14 A B intersection objects that belong to set A and set B objects that belong to set A or set B subset has fewer elements or equal to the set subset has fewer elements than A B union A B subset A B proper subset / strict 9 subset the set 9,14,28 A B not subset left set not a subset of right set 9,66 9,14,28 A B superset set A has more elements or equal 9,14,28 to the set B 9,14,28 A B proper superset / strict set A has more elements than set 9,14,28 superset B 9,14 A B not superset set A is not a superset of set B 9,14,28 9,66 2A power set all subsets of A power set all subsets of A A=3,9,14, A = B equality both sets have the same members B=3,9,14, A=B Ac complement all the objects that do not belong to set A A = 3,9,14, A B relative complement objects that belong to A and not to B B = 1,2,3, A-B = 9,14 A = 3,9,14, A - B relative complement objects that belong to A and not to B B = 1,2,3, A-B = 9,14 A = 3,9,14, A B symmetric difference objects that belong to A or B but B = 1,2,3, not to their intersection A B = 1,2,9,14 A = 3,9,14, A B symmetric difference objects that belong to A or B but B = 1,2,3, not to their intersection A B = 1,2,9,14 aA element of set membership A=3,9,14, 3 A xA not element of no set membership A=3,9,14, 1 A 10 (a,b) A×B |A| #A Ø 0 ordered pair collection of 2 elements set of all ordered pairs from A and B cartesian product cardinality the number of elements of set A A=3,9,14, |A|=3 A=3,9,14, #A=3 cardinality the number of elements of set A aleph-null infinite cardinality of natural numbers set cardinality of countable ordinal numbers set aleph-one empty set universal set natural numbers / whole numbers set (with zero) natural numbers / whole Ø = set of all possible values C = Ø 0 = 0,1,2,3,4,. 0 0 1 numbers set (without zero) 1 = 1,2,3,4,5,. 6 1 integer numbers set = .-3,-2,-1,0,1,2,3,. = x | x=a/b, a,b = x | - < x < = z | z=a+bi, -<a<, -<b< -6 2/6 rational numbers set real numbers set 6.3434346+2i complex numbers set Logic symbols Symbol Symbol Name and caret / circumflex ampersand plus and and and or Meaning / definition Example · & + x · y x y x & y x + y 11 | x' x ¬ ! reversed caret or x y x | y x' x ¬ x ! x x y x vertical line single quote bar not exclamation mark or not - negation not - negation not - negation not - negation circled plus / oplus exclusive or - xor tilde negation implies equivalent if and only if (iff) equivalent if and only if (iff) for all there exists there does not exists therefore because / since Calculus & analysis symbols Symbol Symbol Name Meaning / definition Example limit limit value of a function epsilon represents a very small number, near zero 0 12 e e constant / Euler's e = lim number e = 2.718281828. (1+1/x)x ,x y ' derivative derivative - Lagrange's notation (3x3)' = 9x2 y '' second derivative derivative of derivative (3x3)'' = 18x y(n) nth derivative n times derivation (3x3)(3) = 18 derivative derivative - Leibniz's notation d(3x3)/dx = 9x2 second derivative derivative of derivative d2(3x3)/dx2 = 18x nth derivative n times derivation time derivative derivative by time - Newton's notation time second derivative derivative of derivative Dx y derivative derivative - Euler's notation Dx2y second derivative derivative of derivative partial derivative (x2+y2)/x = 2x integral opposite to derivation f(x)dx double integral integration of function of 2 variables f(x,y)dxdy triple integral integration of function of 3 variables f(x,y,z)dxdydz closed contour / line integral closed surface integral 13 closed volume integral a,b closed interval a,b = x | a x b (a,b) open interval (a,b) = x | a < x < b i imaginary unit i -1 z = 3 + 2i z* complex conjugate z = a+bi z*=a-bi z* = 3 - 2i z complex conjugate z = a+bi z = a-bi z = 3 - 2i nabla / del gradient / divergence operator f (x,y,z) vector unit vector x * y convolution y(t) = x(t) * h(t) Laplace transform F(s) = f (t) Fourier transform X() = f (t) delta function lemniscate infinity symbol 14