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数学符号及表达式英语发音

17.2.1999/H. V¨liaho a

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 pq pq 2. Sets x∈A x∈A / AB AB A∩B A∪B A\B A×B x belongs to A / x is an element (or a member) of A x does not belong to A / x is not an element (or a member) of A A is contained in B / A is a subset of B A contains B / B is a subset of A A cap B / A meet B / A intersection B A cup B / A join B / A union B A minus B / the dierence between A and B A cross B / the cartesian product of A and B there exists for all p implies q / if p, then q p if and only if q /p is equivalent to q / p and q are equivalent

3. Real numbers x+1 x1 x±1 xy (x y)(x + y) x y = x=5 x=5 x plus one x minus one x plus or minus one xy / x multiplied by y x minus y, x plus y x over y the equals sign x equals 5 / x is equal to 5 x (is) not equal to 5 1

x≡y x≡y x>y x≥y x<y x≤y 0<x<1 0≤x≤1 |x| x2 x3 x4 xn x √ x √ 3 x √ 4 x √ n x x y n! x x x xi
n n

x is equivalent to (or identical with) y x is not equivalent to (or identical with) y x is greater than y x is greater than or equal to y x is less than y x is less than or equal to y zero is less than x is less than 1 zero is less than or equal to x is less than or equal to 1 mod x / modulus x x squared / x (raised) to the power 2 x cubed x to the fourth / x to the power four x to the nth / x to the power n x to the (power) minus n (square) root x / the square root of x cube root (of) x fourth root (of) x nth root (of) x x plus y all squared x over y all squared n factorial x hat x bar x tilde xi / x subscript i / x sux i / x sub i

(x + y)2
2

ai
i=1

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 → OA OA AT A1 the norm (or modulus) of x OA / vector OA OA / the length of the segment OA A transpose / the transpose of A A inverse / the inverse of A 2

5. Functions f (x) f :S→T x→y f (x) f (x) f (x) f (4) (x) f x1 2f x2 1
∞ 0 x→0 x→+0 x→0

f x / f of x / the function f of x a function f from S to T x maps to y / x is sent (or mapped) to y f prime x / f dash x / the (rst) derivative of f with respect to x f double–prime x / f double–dash x / the second derivative of f with respect to x f triple–prime x / f triple–dash x / the third derivative of f with respect to x f four x / the fourth derivative of f with respect to x the partial (derivative) of f with respect to x1 the second partial (derivative) of f with respect to x1 the integral from zero to innity

lim

the limit as x approaches zero the limit as x approaches zero from above the limit as x approaches zero from below log y to the base e / log to the base e of y / natural log (of) y log y to the base e / log to the base e of y / natural log (of) y

lim

lim

loge y ln y

Individual mathematicians often have their own way of pronouncing mathematical expressions 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 f x may → be interpreted as any of: f x, f (x), fx , F X, F X, F X . The dierence 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 F X, the length of the segment F X, vector F X. Similarly, a mathematician is unlikely to make any distinction in speech (except sometimes a dierence 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 an1 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

Pronunciation of Mathematical Symbols
Symbols
+ ± x / ÷ = ≈ ≡ ≠ > < ≥ ≤ ⊥ ∣∣
4

plus minus plus or minus multiplied by over; divided by divided equals approximately, similar equivalent to; identical not equal to greater than less than greater than or equal to less than or equal to not greater than not less than much greater than much less than perpendicular to parallel to

/'pls/ /'mans/ /'pls : 'mans/ /'mltplad ba/ /'v/ /d'vadd/ /d'vadd/ /':kwlz/ /'prksmtl/ /'sml t/ /k'wvlnt t/ /a'dentkl t/ /'nt 'ikwl t/ /'gret n/ /'les n/ /'gret n r 'ikwl t/ /'les n r' ikwl t/ /'nt 'gret n/ /'nt 'les n/ /'m 'gret n/ /'m 'les n/ /ppn'dkjl t/ /'prlel t/

not equivalent to, not identical /'nt k'wvlnt t/ /'nt a'dentkl to t/ not similar to squared cubed to the fourth; to the power four /'nt 'sml t/ /'skwed/ /'kju:bd/ /t 'fθ/ /te 'p f/

n

to the n; to the nth; to the power n root; square root cube root fourth root factorial percent infinity varies as; proportional to dot double dot is to, ratio of f; function f dash; derivative f double-dash; second derivative f triple-dash; f treble-dash; third derivative f four; fourth derivative partial derivative, delta integral sum with respect to log log to the base 2 of x therefore because gives, leads to, approaches per

/t en; t d enθ; t pr en/ /ru:t/ /skwe ru:t/ /kju:b ru:t/ /fθ rut/ /fk'trl/ /p'sent/ /n'fnt/ /'vrz/ /pr'pnl/ /dt/ /dbl dt/ /re/ /ef/ /'fkn/ /d/ /d'rvtv/ /'dbl d/ /'seknd d'rvtv/ /'trpl d/ / trebl d/ /θ:d d'rvtv/ /fθ d'rvtv/ /pal d'rvtv/ /delt/ /'ntgrl/ /sm/ /w 'rspekt/ /lg/ /lg t bes tu: v eks/ /'f/ /b'kz/ /gvz/ /li:dz t/ /prz/ /p:/

√ ! % ∞ ∝ ˙ ¨ : f(x) fx f'(x) f''x f'''(x) f(4) ∫ ∑ w.r.t. log logx ∴ ∵ → / ∈

belongs to; a member of; an /b'lz/ /'memb/ /'elmnt/

element of does not belong to; is not a /nt b'l/ /nt 'memb/ /nt n member of; is not an element 'elmnt/ of contained in; a proper subset /kn'tend n/ /'prp 'sbset/ of contained in; subset intersection union for all cos x; cosine x sine x tangent x cosec x shine x cosh x than x mod x; modulus x degrees Centigrade degrees Fahrenheit degrees Kelvin absolute zero /'sbset/ /'ntsekn/ /'junn/ /f r:l/ /kz/ /san/ /tan/ /'ksek/ /'an/ /'k/ /θn/ /md/ /'mdjls/ /d'gri:z 'sentgred/ /d'gri:z 'frnhat/ /d'gri:z 'kelvn/ /abslu:t zi:r/

cos x sin x tan x cosec x sinh x cosh x tanh x |x| ℃ ℉ °K 0°K, –273.15 °C mm cm

millimetre centimetre

/'mlmit/ /'sentmit/ /'kjubk 'sentmit/ /'sentmit 'kju:bd/ /'mit/ /k'lmt/ '/mlgrm/

cc, cm

cubic centimetre, centimetre cubed

m km mg

metre kilometre milligram

g kg AC DC

gram kilogram A.C. D.C.

/grm/ /'klgrm/ /e si:/ /di: si:/

Examples
x+1 x -1 x±1 xy (x — y)(x + y) x/y x÷y x=5 x≈y x≡y x≠y x>y x<y x≥y x≤y 0<x<1 0≤x≤1 x x x x x
4 n -n

x plus one x minus one x plus or minus one x y; x times y; x multiplied by y x minus y, x plus y x over y; x divided by y; x divided by y x equals 5; x is equal to 5 x is approximately equal to y x is equivalent to y; x is identical with y x is not equal to y x is greater than y x is less than y x is greater than or equal to y x is less than or equal to y zero is less than x is less than 1; x is greater than zero and less than 1 zero is less than or equal to x is less than or equal to 1; x is greater than or equal to zero and less than or equal to 1 x squared x cubed x to the fourth; x to the power four x to the n; x to the nth; x to the power n x to the minus n; x to the power of minus n root x; square root x; the square root of x the cube root of x the fourth root of x



the nth root of x (x + y) (x/y) n! x% ∞ x ∝ y f(x) fx f'(x) f''x f'''(x) f(4) v v θ v θ dv dv dθ dv dθ ∫ x plus y all squared x over y all squared n factorial; factorial n x percent infinity x varies as y; x is (directly) proportional to y x dot x double dot f of x; the function of x f dash x; the (first) derivative of with respect to x f double-dash x; the second derivative of f with respect to x f triple-dash x; f treble-dash x; the third derivative of f with respect to x f four x; the fourth derivative of f with respect to x the partial derivative of v delta v by delta theta, the partial derivative of v with respect to θ delta two v by delta theta squared; the second partial derivative of v with respect to θ the derivative of v d v by d theta, the derivative of v with respect to theta d 2 v by d theta squared, the second derivative of v with respect to theta, integral integral from zero to infinity ∑ sum the sum from i equals 1 to n w.r.t. logey ∴ with respect to log to the base e of y; log y to the base e; natural log (of) y therefore

x ∝ 1/y x varies as one over y; x is indirectly proportional to y

∵ → Δx → 0 lim
Δx→0

because gives, approaches delta x approaches zero the limit as delta x approaches zero, the limit as delta x tends to zero the limit as delta x approaches zero, the limit as delta x tends to zero metres per second x belongs to A; x is a member of A; x is an element of A x does not belong to A; x is not a member of A; x is not an element of A A is contained in B; A is a proper subset of B A is contained in B; A is a subset of B A intersection B A union B cos x; cosine x sine x tangent x, tan x cosec x shine x cosh x than x mod x; modulus x eighteen degrees Centigrade seventy degrees Fahrenheit

Lt
Δx→0

m/sec x ∈ A x A A B A B AB AB cos x sin x tan x cosec x sinh x cosh x tanh x |x| 18 ℃ 70 ℉

Greek alphabet
Α α alpha Β β beta Δ δ delta /'lf/ /'bi:t/ /'delt/

Γ γ gamma /'gm/ Ε ε epsilon /'epsiln/ Ζ ζ zeta /'zit/

Η η eta Θ θ theta Ι ι iota

/'it/ /'θit/ /a't/ /'kp/ /'lmd/ /'mju/ /'nju/ /'ksa/ /'pa/ /'r/ /'sgm/ /'t/ /'fa/ /'ka/ /'psa/

Κ κ kappa ∧ λ lamda Μ μ mu Ν ν nu Ξ ξ xi ∏ π pi Ρ ρ rho ∑ σ sigma Τ τ tau

Ο ο omicron /'mkrn

Υ υ upsilon /'jpsln/ Φ φ phi Χ χ chi Ψ ψ psi

ω omega /'mg

Fractions
a half a quarter / 'h:f/ / 'kwt/

three quarters /θri 'kwtz/ a third two thirds a fifth two fifths three fifths / 'θ:d/ /tu: 'θ:dz/ / 'ffθ/ /tu: 'ffθs/ /θri 'ffθs/

four fifths a sixth five sixths an eighth

/f 'ffθs/ / 'sksθ/ /fav 'sksθs/ /n 'etθ/

three eighths /θri 'etθs/ five eighths /fav 'etθs/

seven eighths /sevn 'etθs/

Decimal Fractions
0.1 0.01 0.0001 1.1 1.2 1.23 1.0123 10.01 21.57 2.6666666666.... 2.612361236123... 2.5 million nought point one nought point oh one one point one one point two one point two three ten point oh one twenty-one point five seven two point six recurring /n:t pnt wn/ /n:t pnt wn/ /wn pnt wn/ /wn pnt tu:/ /wn pnt tu: θri:/ /ten pnt wn/ /'twent wn pnt fav 'sevn/ /tu: pnt sks r'k:r/

nought point oh oh oh one /ten pnt wn/

one point oh one two three /wn pnt wn tu: θri:/

two point six one two three /tu: pnt sks wn tu: θri: recurring r'k:r/ two point five million /tu: pnt fav 'mljn/

SI Units: Prefixes
10-24 yocto y /j'kt/ 10-21 zepto z /'zept/ 10-18 atto 10 10 10
-15 -12 -9

a /'at/ p /'pi:k/

femto f /'femt/ pico nano n /'nan/

10-6 micro /'makr/ 10-3 milli 10-1 deci 103 kilo m /'ml/ d /'des/ k /'kl/ 10-2 centi c /'sent/

106 mega M /'meg/ 109 giga G /'gi:g/ 1012 tera 1018 exa T /'ter/ E /'eks/ 1015 peta P /'pet/ 1021 zeta Z /'zet/ 1024 yota Y /'jt/

Cardinal Numbers
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen /wn/ /tu:/ /θri:/ /f/ /fav/ /sks/ /'sevn/ /et/ /nan/ /ten/ /'levn/ /twelv/ /θ:'ti:n/ /f'ti:n/ /ff'ti:n/ /skst'i:n/ /seven'ti:n/ /e'ti:n/

19 20 21 22 23 24 25 26 27 28 29 30 40 50 60 70 80 90 100 101 102 110 120 200 300 400 500 600 700 800 900 1 000

nineteen twenty twenty-one twenty-two twenty-three twenty-four twenty-five twenty-six twenty-seven twenty-eight twenty-nine thirty forty fifty sixty seventy eighty ninety a hundred; one hundred a hundred and one a hundred and two a hundred and ten a hundred and twenty two hundred three hundred four hundred five hundred six hundred seven hundred eight hundred nine hundred a thousand, one thousand

/nan'ti:n/ /'twent/ /twent'wn/ /twent'tu:/ /twent'θri:/ /twent'f/ /twent'fav/ /twent'sks/ /twent'sevn/ /twent'et/ /twent'nan/ /'θ:t/ /'ft/ /'fft/ /'skst/ /'sevent/ /'et/ /'nant/ / 'hndrd/ /wn 'hndrd/ / 'hndrd n wn/ / 'hndrd n tu:/ / 'hndrd n ten/ / 'hndrd n 'twent/ /tu: 'hndrd/ /θri: 'hndrd/ /f 'hndrd/ /fav 'hndrd/ /sks 'hndrd/ /'sevn 'hndrd/ /et 'hndrd/ /nan 'hndrd/ / θ'znd/ /wn 'θznd/

1 001 1 010 1 020 1 100 1 101 1 110 9 999 10 000 15 356 100 000 100 000 000

a thousand and one a thousand and ten a thousand and twenty one thousand, one hunded one thousand, one hundred and one one thousand, one hundred and ten nine thousand, nine hundred and ninety-nine ten thousand fifteen thousand, three hundred and fifty six a hundred thousand

/ 'θznd n wn/ / 'θznd n ten/ / 'θznd n 'twent/ /wn 'θznd wn 'hndrd/ /wn 'θznd wn 'hndrd n wn/ /wn 'θznd wn 'hndrd n ten/ /nan 'θznd nan 'hndrd n 'nant 'nan/ /ten 'θznd/ /'ffti:n 'θznd θri: 'hndrd n 'fft sks/ / 'hndrd 'θznd/ / 'mljn/ / 'hndrd 'mljn/ / 'bljn/ / 'hndrd 'bljn/ / 'trljn/

1 000 000 a million a hundred million

1 000 000 a billion 000 100 000 000 000 a hundred billion

1 000 000 a trillion 000

Ordinal Numbers
1st 3rd 4th 5th 6th 7th 8th 9th first third fourth fifth sixth seventh eighth ninth /f:st/ /'seknd/ /θ:d/ /f:θ/ /ffθ/ /sksθ/ /'sevnθ/ /etθ/ /nanθ/ /tenθ/

2nd second

10th tenth

11th eleventh 12th twelfth 13th thirteenth 14th fourtheenth 15th fidteenth 16th sixteenth 17th seventeenth 18th eighteenth 19th nineteenth 20th twentieth 21st twenty-first 23rd twenty-third 24th twenty-fourth 25th twenty-fifth 26th twenty-sixth 28th twenty-eighth 29th twenty-ninth 30th thirtieth 31st thirty-first

/'levnθ/ /'twelfθ/ /θ:'ti:nθ/ /f'ti:nθ/ /ff'ti:nθ/ /sks'ti:nθ/ /seven'ti:nθ/ /e'ti:nθ/ /nan'ti:nθ/ /'twentθ/ /twent'f:st/ /twent'θ:d/ /twent'f:θ/ /twent'ffθ/ /twent'sksθ/ /twent'etθ/ /twent'nanθ/ /'θtθ/ /θt'f:st/

22nd twenty-second /twent'seknd/

27th twenty-seventh /twent'sevnθ/