常用数学公式（符号）读法.pdf

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Pronunciation of mathematical expressions
. ]' P* Y; s# ]" n2 D9 `$ ZThe pronunciations of the most common mathematical expressions are given in the list
9 s$ r7 g6 g" @. Z  {3 ]below. In general, the shortest versions are preferred (unless greater precision is necessary).
6 }" h/ J' S% Q0 e2 Z7 [1. Logic
" X& R# d' U5 V& g, Q9 there exists
& m' n* ?3 F- d9 j) I* ^. a8 for all
p ) q p implies q / if p, then q
9 O2 X" r) j, {* up , q p if and only if q /p is equivalent to q / p and q are equivalent
" a# @! g7 @9 }$ [9 l  F2 ?9 t6 ~2. Sets
x 2 A x belongs to A / x is an element (or a member) of A
4 F0 u* ~# ~9 P$ A1 ]9 Q  ax =2 A x does not belong to A / x is not an element (or a member) of A
+ m0 }7 b( ?5 k* H+ T; n" BA 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
7 K4 x4 X4 `) g, lA \ B A cap B / A meet B / A intersection B
A [ B A cup B / A join B / A union B
A n B A minus B / the di®erence between A and B
3 G4 m7 d: g  hA £ B A cross B / the cartesian product of A and B
! R' m. z9 }% V- S3. Real numbers
x + 1 x plus one
  j6 N0 x' {: i2 p: ax ¡ 1 x minus one
$ f8 q. j; I' p( h8 L6 ?# d4 ix § 1 x plus or minus one
+ _& Y6 u+ O# R# u- |9 \* Txy xy / x multiplied by y
1 ~: u) |: x- ^2 {4 |1 e(x ¡ y)(x + y) x minus y, x plus y
x
y
x over y
0 k3 Q7 y/ I4 x8 O8 ?= the equals sign
2 H+ O- B& Q( n1 o9 B; Ix = 5 x equals 5 / x is equal to 5
7 F2 L$ P7 x) ~0 w. X: S' vx 6= 5 x (is) not equal to 5
0 `- a7 ]3 O% ~  ]) _7 m1
x ´ y x is equivalent to (or identical with) y
5 @- ?$ E. C5 |+ `$ }% g- Kx 6´ y x is not equivalent to (or identical with) y
0 R: ?+ d/ t! ^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
5 c( U: u) D$ `$ c: d0 < 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
x2 x squared / x (raised) to the power 2
  T2 g  ~9 r1 Z$ yx3 x cubed
- M% V# A' N2 Q1 f: m! wx4 x to the fourth / x to the power four
7 F. i0 q2 M' p) q# ixn x to the nth / x to the power n
- q8 U& W. ^4 K- Ux&iexcl;n x to the (power) minus n
9 [: v& F' w; n; q. j# t$ W2 g' ipx (square) root x / the square root of x
, c$ l2 @9 ^1 o% |! F, T/ G, o+ p# h. np3 x cube root (of) x
# k8 p! l1 m2 Q- r; \8 \p4 x fourth root (of) x
npx nth root (of) x
, F% Q! C9 `! P(x + y)2 x plus y all squared
6 g- d( N# o7 g* e% ~) ]&sup3;x
y
- N; `4 x7 b9 t; M) ^$ ^4 M&acute;2
x over y all squared
3 t. p- E& p8 ~5 H2 Y$ T# Sn! n factorial
^x x hat
&sup1;x x bar
~x x tilde
xi xi / x subscript i / x su±x i / x sub i
Xn
i=1
1 M* h" g% `; w5 `1 Iai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai
4. Linear algebra
kxk the norm (or modulus) of x
O&iexcl;&iexcl;!A OA / vector OA
( E9 H: k/ ]/ _  i! W3 x$ oOA OA / the length of the segment OA
AT A transpose / the transpose of A
: X4 d) }' h. }A&iexcl;1 A inverse / the inverse of A
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5. Functions
* f! _9 [& m7 @' _  ]$ q; yf(x) fx / f of x / the function f of x
& J) {, h9 G$ i" m& U, uf : S ! T a function f from S to T
; _" _$ B1 R2 g1 ]x 7! y x maps to y / x is sent (or mapped) to y
2 O9 B/ c  t, f, Y0 jf0(x) f prime x / f dash x / the (&macr;rst) derivative of f with respect to x
5 p# h! j) @$ g; V: `f00(x) f double{prime x / f double{dash x / the second derivative of f with
respect to x
+ i6 R# h4 C0 P+ P4 Vf000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect
: V% A. y' f) B7 T' ~to x
$ f: b, O; T* a2 L9 |f(4)(x) f four x / the fourth derivative of f with respect to x
@f
@x1
# b' \8 C/ x8 \the partial (derivative) of f with respect to x1
5 V2 Z6 F4 N" O@2f
@x21
the second partial (derivative) of f with respect to x1
Z
- Q( a; U" B) r* n( j1
6 ^6 ~. d) J+ {' F) r0
the integral from zero to in&macr;nity
% g2 a, X9 t+ ilim
x!0
the limit as x approaches zero
lim
  P  l& K4 t* V# L% @# Tx!+0
  [4 W3 o3 T* b3 X/ A2 lthe limit as x approaches zero from above
lim
( `" Y( x$ P- o: M) ]x!&iexcl;0
& b4 ]; A8 r; K0 a; f$ O* Pthe 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
4 L% y6 K& c8 @1 @5 {Individual mathematicians often have their own way of pronouncing mathematical expressions
4 a5 z7 @; ]' @( P1 s& j7 uand in many cases there is no generally accepted \correct" pronunciation.
: F" z  X& ?; p( n2 vDistinctions 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
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
* {: @% P6 ]& f) M9 m  Q1 B+ J8 Ya di&reg;erence in intonation or length of pauses) between pairs such as the following:
x + (y + z) and (x + y) + z
pax + b and pax + b
an &iexcl; 1 and an&iexcl;1
The primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science
9 r6 j2 C* T8 h8 Hand Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have
+ `! H' t- T& R- S9 U& ?$ }given good comments and supplements.
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