数学公式的英语读法-Reading_maths_Symbols

Common Symbols of Mathematics and Their Meaning and Reading in English ∗ Zhengsheng Wang† Department of Mathematics, Nanjing University of Aeronautics and Astronautics 29 Yudao Street, Nanjing 210016, P.R. China Abstract We often use the symbols in mathematical formulas. We may know their meanings and their reading in Chinese, But we may not know how to read them in English. And this is very important for a teacher to teach and report in English. In this paper, we discuss the how to read the common symbols of mathematics in English. Keywords: Symbols of mathematics; Reading in English 1. Introduction We often use the symbols in mathematical formulas. We may know their meanings and their reading in Chinese, But we may not know how to read them in English. And this is very important for a teacher to teach and report in English. In this paper, we discuss the how to read the common symbols of mathematics in English. In section 2, the reading will be listed in a table. Some examples are given in Section 3. 2. The Meaning and Reading of Common Mathematical Sym- bols in English Symbols Meaning and Reading + plus, positive − minus, negative ± plus or minus × multiplied by, times ÷ divided by = is equal to, equals ≈ is approximately equal to, approximately equals ∈ is member of set ⊂ is subset of set ⇔ is equivalent to ⇒ implies ∗This paper was finished during the visit of the author to The University of Melbourne in Australia in 2005. †E-mail address: wangzhengsheng@nuaa.edu.cn (Z.S.Wang). 1 TABLE 1. Common Symbols of Mathematics and Their Reading in English. Symbols Meaning and Reading∑ sigma, the sum of the terms indicated∏ the product of the terms indicated ∞ infinity φ the empty set Q the set of rational numbers R the set of real numbers C the set of complex numbers a 6= b a is not equal to b a > b(<) a is greater (less) than b a ≥ b(≤) a is greater than or equal to b a >> b(<<) a is much greater(less) than b a b a divided by b, a bth ap a to the power p a 1 2 a to the power 12 , square root of a a 1 n a to the power 1n , nth root of a |a| the absolute of a n! factorial n TABLE 2. Common Symbols of Mathematics and Their Reading in English. Symbols Meaning and Reading df dx , df/dx, f ′, Df derivative of the function f with respect to x ∂f ∂x , ∂f/∂x, ∂xf,Dxf partial derivative of the function f with respect to x, where f is a function of x and another variable dnf dxn , d nf/dxn, f (n), D(n)f nth derivative of the function f with respect to x ( dfdx)x=a value at a of the derivative of the function f df total differential of the function f∫ f(x)dx an indefinite integral of the function f∫ b a f(x)dx definite integral of the function f from a to b ex, exp(x) exponential function to the base e of x logax logarithm to the base a of x lnx nature logarithm of x lgx common logarithm of x TABLE 3. Common Symbols of Mathematics and Their Reading in English. 2 Symbols Meaning and Reading sinx sine of x cosx cosine of x tanx, tgx tangent of x cotx, ctgx cotangent of x i imaginary unit, i2 = −1 Re(z) real part of z Im(z) imaginary part of z arg(z) argument of z a · b scalar product of a and b a× b vector product of a and b TABLE 4. Common Symbols of Mathematics and Their Reading in English. 3. Examples Formulas Meaning and Reading 3 + 13 = 3 1 3 three plus one third is equal to three and one third 2.35× 2 = 4.70 two point three five times 2 makes four point seven zero x2 + y2 = 10 x squared and y squared equals ten 21÷ 6 = 3and3 three into twenty one goes three and three remainder 2 two per cent 3 8 three eighths per mille d2f dx2 − ∂g∂y = 0 second derivative of function f with respect to x plus partial derivative of function g with respect to y equals zero TABLE 5. Examples of Common Symbols of Mathematics and Their Reading in English. Acknowledgements The author would like to thank the references for their valuable comments that led to improvements of the paper. References [1] A Mathematical Dictionary in English. [2] . 3 17.2.1999/H. Va¨liaho Pronunciation of mathematical expressions The pronunciations of the most common mathematical expressions are given in the list below. In general, the shortest versions are preferred (unless greater precision is necessary). 1. Logic ∃ there exists ∀ for all p⇒ q p implies q / if p, then q p⇔ q p if and only if q /p is equivalent to q / p and q are equivalent 2. Sets x ∈ A x belongs to A / x is an element (or a member) of A x /∈ A x does not belong to A / x is not an element (or a member) of A A ⊂ B A is contained in B / A is a subset of B A ⊃ B A contains B / B is a subset of A A ∩B A cap B / A meet B / A intersection B A ∪B A cup B / A join B / A union B A \B A minus B / the difference between A and B A×B A cross B / the cartesian product of A and B 3. Real numbers x+ 1 x plus one x− 1 x minus one x± 1 x plus or minus one xy xy / x multiplied by y (x− y)(x+ y) x minus y, x plus y x y x over y = the equals sign x = 5 x equals 5 / x is equal to 5 x 6= 5 x (is) not equal to 5 1 x ≡ y x is equivalent to (or identical with) y x 6≡ y x is not equivalent to (or identical with) y x > y x is greater than y x ≥ y x is greater than or equal to y x < y x is less than y x ≤ y x is less than or equal to y 0 < x < 1 zero is less than x is less than 1 0 ≤ x ≤ 1 zero is less than or equal to x is less than or equal to 1 |x| mod x / modulus x x2 x squared / x (raised) to the power 2 x3 x cubed x4 x to the fourth / x to the power four xn x to the nth / x to the power n x−n x to the (power) minus n √ x (square) root x / the square root of x 3 √ x cube root (of) x 4 √ x fourth root (of) x n √ x nth root (of) x (x+ y)2 x plus y all squared(x y )2 x over y all squared n! n factorial xˆ x hat x¯ x bar x˜ x tilde xi xi / x subscript i / x suffix i / x sub i n∑ i=1 ai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai 4. Linear algebra ‖x‖ the norm (or modulus) of x −−→ OA OA / vector OA OA OA / the length of the segment OA AT A transpose / the transpose of A A−1 A inverse / the inverse of A 2 5. Functions f(x) fx / f of x / the function f of x f : S → T a function f from S to T x 7→ y x maps to y / x is sent (or mapped) to y f ′(x) f prime x / f dash x / the (first) derivative of f with respect to x f ′′(x) f double–prime x / f double–dash x / the second derivative of f with respect to x f ′′′(x) f triple–prime x / f triple–dash x / the third derivative of f with respect to x f (4)(x) f four x / the fourth derivative of f with respect to x ∂f ∂x1 the partial (derivative) of f with respect to x1 ∂2f ∂x21 the second partial (derivative) of f with respect to x1∫ ∞ 0 the integral from zero to infinity lim x→0 the limit as x approaches zero lim x→+0 the limit as x approaches zero from above lim x→−0 the limit as x approaches zero from below loge y log y to the base e / log to the base e of y / natural log (of) y ln y log y to the base e / log to the base e of y / natural log (of) y Individual mathematicians often have their own way of pronouncing mathematical expres- sions and in many cases there is no generally accepted “correct” pronunciation. Distinctions made in writing are often not made explicit in speech; thus the sounds fx may be interpreted as any of: fx, f(x), fx, FX, FX, −−→ FX . The difference is usually made clear by the context; it is only when confusion may occur, or where he/she wishes to emphasise the point, that the mathematician will use the longer forms: f multiplied by x, the function f of x, f subscript x, line FX, the length of the segment FX, vector FX. Similarly, a mathematician is unlikely to make any distinction in speech (except sometimes a difference in intonation or length of pauses) between pairs such as the following: x+ (y + z) and (x+ y) + z √ ax+ b and √ ax+ b an − 1 and an−1 The primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science and Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have given good comments and supplements. 3