常用数学公式（符号）读法.pdf

lilianjie

Pronunciation of mathematical expressions
  K1 j  ~: _* S# D$ j) }% {9 Q6 aThe 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).
6 |( x4 u4 D$ ]# h1. Logic
9 there exists
8 for all
8 `! @  F' j/ H8 g: |7 up ) q p implies q / if p, then q
+ `4 c, n, E6 V1 xp , q p if and only if q /p is equivalent to q / p and q are equivalent
) M8 ~# v/ u) {2. Sets
x 2 A x belongs to A / x is an element (or a member) of A
x =2 A x does not belong to A / x is not an element (or a member) of A
A ½ B A is contained in B / A is a subset of B
3 u; N, h* g# K5 pA ¾ B A contains B / B is a subset of A
: o' I0 m! Y' zA \ B A cap B / A meet B / A intersection B
  }; h5 F+ Q) q1 k; P7 w) O( D: M9 ^A [ B A cup B / A join B / A union B
A n B A minus B / the di®erence between A and B
" }# l+ ~( q2 B! p  K' E, FA £ B A cross B / the cartesian product of A and B
3. Real numbers
* L- N/ K# O( N) Q3 Cx + 1 x plus one
x ¡ 1 x minus one
8 C2 \$ w4 j1 l0 D" O7 ox § 1 x plus or minus one
xy xy / x multiplied by y
(x ¡ y)(x + y) x minus y, x plus y
0 J) ?' o* B9 D9 ^# k+ d: a& f! ^x
y
9 c, e6 x. N4 T  \8 h1 R9 Px over y
4 Z! C! R3 o: f  w= the equals sign
x = 5 x equals 5 / x is equal to 5
x 6= 5 x (is) not equal to 5
: l" g2 k# x  D$ a' R1 k* i$ k1
6 `5 s1 f% t1 n9 k" V7 ix ´ y x is equivalent to (or identical with) y
# @0 t3 O& J: o, \) D# R5 [8 ?x 6´ y x is not equivalent to (or identical with) y
x > y x is greater than y
! r9 b9 v& G) r/ }) Rx ¸ y x is greater than or equal to y
  e% p5 h9 a1 _! E0 y) y2 Yx < y x is less than y
% j7 e% n+ r2 U' X& Ax · y x is less than or equal to y
8 `0 ?- _' D* t) U0 < 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
( s! f! c2 L4 A. x" ]x2 x squared / x (raised) to the power 2
0 D" n( b4 M; l: B/ {- j4 ex3 x cubed
x4 x to the fourth / x to the power four
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
p3 x cube root (of) x
p4 x fourth root (of) x
- m' }; I& A/ M8 u2 Enpx nth root (of) x
(x + y)2 x plus y all squared
&sup3;x
y
. {5 r& x0 z" \$ N9 m; R  z6 o# h&acute;2
x over y all squared
n! n factorial
^x x hat
  x, T0 Z, ?$ m" w7 ]% `7 y&sup1;x x bar
3 O- q4 J1 m; X( q1 p~x x tilde
/ ]- l3 A/ n" y, A/ ?! `xi xi / x subscript i / x su±x i / x sub i
" z& L0 _  ?9 c: _Xn
i=1
ai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai
% i: |# ^7 M+ G: R# i8 L7 w9 M4. Linear algebra
kxk the norm (or modulus) of x
O&iexcl;&iexcl;!A OA / vector OA
# ^1 g( H/ @! a* W8 TOA OA / the length of the segment OA
) V4 I5 o4 n, u1 G; TAT A transpose / the transpose of A
A&iexcl;1 A inverse / the inverse of A
2
5. Functions
f(x) fx / f of x / the function f of x
& G5 S' \% c% t/ W7 X. }f : S ! T a function f from S to T
$ y% }$ c5 A  @& {x 7! y x maps to y / x is sent (or mapped) to y
  S$ b" [3 r- P1 W; \& S5 l9 L! zf0(x) f prime x / f dash x / the (&macr;rst) derivative of f with respect to x
f00(x) f double{prime x / f double{dash x / the second derivative of f with
respect to x
: s1 e, }7 ]) N% g1 N1 `* Q$ U  Pf000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect
to x
& G9 D7 h" }/ O7 y- Of(4)(x) f four x / the fourth derivative of f with respect to x
1 d: x+ G. ~. G3 S7 y@f
: b6 _' j! _; g( |  y@x1
the partial (derivative) of f with respect to x1
2 [. U/ A$ j  {) Q" u@2f
@x21
  I2 Y* ~" |# y7 k6 W# o/ N* [the second partial (derivative) of f with respect to x1
2 U" g( j. v% U7 W5 lZ
1
3 R7 j! x* ]7 {& ^: [1 E9 ^0
7 {! Z; O5 q6 Bthe integral from zero to in&macr;nity
lim
* B$ u% ]2 X: e- wx!0
, `+ g6 X& ]5 S3 bthe limit as x approaches zero
lim
: M( `8 t8 R: z. E+ ]9 M2 `& jx!+0
- C1 }1 I9 e* e- H* a, kthe limit as x approaches zero from above
" W: t9 C; |. e; n. k4 e3 Z, }# ~lim
- G+ w4 w, i. q1 G8 ^x!&iexcl;0
( O, {& K) {: Z( q! Sthe 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 expressions
4 J* r) u( d9 Cand 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
% L8 F! l' [" p/ ?" n8 Nbe 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
" W8 r! _; `  i( F" d( F, f  Q6 E' hf 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
9 h& m$ j, n, g( Y% w' @3 t, c6 P4 Ya di&reg;erence in intonation or length of pauses) between pairs such as the following:
x + (y + z) and (x + y) + z
6 |6 ^- F! l! a$ Mpax + 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
and Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have
4 R* p- M- K4 ggiven good comments and supplements.
! E( H; M6 K1 E2 J+ l3

lilianjie

NO常用数学公式

孤寂冷逍遥

yt@A