常用数学公式（符号）读法.pdf

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Pronunciation of mathematical expressions
The pronunciations of the most common mathematical expressions are given in the list
& Z* S9 o* f1 u0 ]below. In general, the shortest versions are preferred (unless greater precision is necessary).
4 e/ X- u1 \3 B1. Logic
9 there exists
8 for all
p ) q p implies q / if p, then q
6 Y( `4 C! u# V) }p , q p if and only if q /p is equivalent to q / p and q are equivalent
2. Sets
4 D; V( C5 G: \* B8 wx 2 A x belongs to A / x is an element (or a member) of A
5 }) k* }; I3 j4 F+ \% o9 X) Vx =2 A x does not belong to A / x is not an element (or a member) of A
& A1 |  H9 |( T6 ]& [A ½ B A is contained in B / A is a subset of B
A ¾ 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
5 u4 W' t+ ^% i7 k! T' E( n- bA n B A minus B / the di®erence between A and B
; `5 H# D, H! T0 R; i, BA £ B A cross B / the cartesian product of A and B
& r3 Y' V1 ^$ }4 n) L+ M4 q1 L3. Real numbers
x + 1 x plus one
9 U& j) {; i. W* Q5 |+ _8 U- Xx ¡ 1 x minus one
8 z' y, T+ [; r. L) Sx § 1 x plus or minus one
) q  ~3 t. v% axy xy / x multiplied by y
(x ¡ y)(x + y) x minus y, x plus y
1 h+ d: ?; ^, G: sx
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
  a( _) r2 @5 b' d. [1
x ´ y x is equivalent to (or identical with) y
- W! i3 C5 g& w) v, ix 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
- E$ x0 Q( t3 S. Q  V& Hx · 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
jxj mod x / modulus x
2 p6 `* R1 }. z5 c2 Sx2 x squared / x (raised) to the power 2
x3 x cubed
x4 x to the fourth / x to the power four
% X- G% X! s# M8 x- _2 v  }xn x to the nth / x to the power n
x&iexcl;n x to the (power) minus n
px (square) root x / the square root of x
" N) t* P; \4 |9 v4 B' qp3 x cube root (of) x
p4 x fourth root (of) x
npx nth root (of) x
(x + y)2 x plus y all squared
&sup3;x
y
# f; W( T  I' v5 q&acute;2
  \' J4 o- K" M) Y1 M) i; ?5 ux over y all squared
n! n factorial
^x x hat
&sup1;x x bar
6 |, H) T0 N( M& W~x x tilde
& F: Q) Y' ?1 p1 ]xi xi / x subscript i / x su±x i / x sub i
Xn
& a+ V& ?1 o. ^9 B# ?- Ai=1
( L8 j& d/ T/ \4 `/ P+ E6 S3 p/ tai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai
; P! `8 \) a4 z# T9 [2 q- v5 T' ]4. Linear algebra
kxk the norm (or modulus) of x
! A1 }) k8 i( D. k/ O; L5 k& I0 _, _0 CO&iexcl;&iexcl;!A OA / vector OA
' R5 w6 h, U8 A0 l! LOA OA / the length of the segment OA
AT A transpose / the transpose of A
! \4 F, u* n& Q% _" C$ a* ]A&iexcl;1 A inverse / the inverse of A
2
3 m) G" N: V9 A1 b5. Functions
f(x) fx / f of x / the function f of x
' F+ y6 ]- C/ B' {( ?# O9 X5 \3 Rf : S ! T a function f from S to T
" b. |4 R- j) W: C$ t& Q4 D( |3 d7 vx 7! y x maps to y / x is sent (or mapped) to y
2 v  }% o; p+ \+ _/ T2 q0 T$ Pf0(x) f prime x / f dash x / the (&macr;rst) derivative of f with respect to x
& J' P9 C0 r$ |( O! U* A: Df00(x) f double{prime x / f double{dash x / the second derivative of f with
respect to x
f000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect
to x
/ _) }  {$ m, X, G! A" e/ x8 Wf(4)(x) f four x / the fourth derivative of f with respect to x
@f
  o; Q/ n  O: o* G4 j@x1
the partial (derivative) of f with respect to x1
% e0 O6 o. c! I; O@2f
@x21
the second partial (derivative) of f with respect to x1
Z
0 z! I" j5 n$ @1
0
+ O, B( S" g8 \  }1 Uthe integral from zero to in&macr;nity
3 J' v$ K; h. [. R- w/ q, C+ klim
- a4 ]6 K$ A. m8 O& N* d7 Vx!0
the limit as x approaches zero
5 n7 t; f2 Q9 a- Mlim
x!+0
* _4 u5 V1 X% L  K  Sthe limit as x approaches zero from above
lim
x!&iexcl;0
" V, y9 c- d6 K# p1 t" Xthe limit as x approaches zero from below
; C' K. s* [5 F$ ?, zloge 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 expressions
. `% b/ E- W  e) i) [and in many cases there is no generally accepted \correct" pronunciation.
7 i7 x# y+ G+ w9 \( E; |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, F&iexcl;&iexcl;X!. The di&reg;erence is usually made clear
" E9 u- [- F; ]( Z) [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.
  U  h2 u2 R6 Z! D: V% ^Similarly, a mathematician is unlikely to make any distinction in speech (except sometimes
a di&reg;erence in intonation or length of pauses) between pairs such as the following:
x + (y + z) and (x + y) + z
; \. @# [. k  epax + b and pax + b
an &iexcl; 1 and an&iexcl;1
  J) `! o8 B' X) F6 w; @The primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science
' c) D) @' T  Q" S5 Jand Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have
given good comments and supplements.
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