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
below. In general, the shortest versions are preferred (unless greater precision is necessary).
; R1 \; U+ [/ j. ]) y" B) x1. Logic
9 there exists
8 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 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
A ¾ B A contains B / B is a subset of A
8 S, t1 l  X/ ~$ x( m3 g% d; a) uA \ B A cap B / A meet B / A intersection B
A [ B A cup B / A join B / A union B
3 h+ v% B3 {7 N' i, AA n B A minus B / the di®erence between A and B
A £ B A cross B / the cartesian product of A and B
- ], \& w. f3 c" h$ [- K/ G3. Real numbers
x + 1 x plus one
x ¡ 1 x minus one
3 Q3 C; E% c. f) G) ~, ex § 1 x plus or minus one
xy xy / x multiplied by y
. b/ m4 [- j2 j/ B* i(x ¡ y)(x + y) x minus y, x plus y
x
8 k: X: E3 H+ w5 ?2 g4 {y
1 q" `( q  Y: A; B) lx over y
% b9 s& Q( M- O5 z, }1 L! d= the equals sign
x = 5 x equals 5 / x is equal to 5
4 s1 J! Y* n% u8 F! m5 ?+ lx 6= 5 x (is) not equal to 5
5 h0 |6 Z% l) r0 U  _6 R1
+ z, a  x6 N( w) N. Hx ´ y x is equivalent to (or identical with) y
7 t2 t! \& F7 D" f1 U$ a7 [8 i+ wx 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
) U1 \5 a* t5 m5 r% b9 N% I3 h$ K5 A0 < 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
! U' Y# R9 t6 @) ~  @$ Z' }jxj mod x / modulus x
7 W3 R$ P4 d% S. @" Jx2 x squared / x (raised) to the power 2
; S6 [7 o+ U7 a! a' ^5 jx3 x cubed
x4 x to the fourth / x to the power four
xn x to the nth / x to the power n
- E5 u! p8 `/ Z/ ~0 p) e# D9 rx&iexcl;n x to the (power) minus n
px (square) root x / the square root of x
' R' ]' }0 F3 S: X% R: o9 [p3 x cube root (of) x
6 i9 Y7 K+ t# P' Jp4 x fourth root (of) x
8 d1 n5 F5 \+ i+ P3 r) w( pnpx nth root (of) x
(x + y)2 x plus y all squared
&sup3;x
y
&acute;2
+ J' c( \% L4 y  G# Cx over y all squared
5 F4 L* y6 Y5 C' F6 I, 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
6 G2 U/ b# j, O5 J0 |Xn
i=1
0 l; q6 f: Q0 |* V7 w7 [8 Y0 eai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai
# x" n( b* t" N9 s/ I& S# {4. Linear algebra
kxk the norm (or modulus) of x
" t6 V6 Y% Y  j2 f$ FO&iexcl;&iexcl;!A OA / vector OA
OA OA / the length of the segment OA
AT A transpose / the transpose of A
A&iexcl;1 A inverse / the inverse of A
2
& |( n3 U1 x0 x- L5. Functions
f(x) fx / f of x / the function f of x
1 B  I/ X! Y6 q. }7 K- nf : S ! T a function f from S to T
8 Z9 g. X' n/ J- mx 7! y x maps to y / x is sent (or mapped) to y
f0(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
, Q6 U0 R6 x4 H; h* \7 N. [4 g$ orespect to x
: f# ^2 ~7 |- e! Z9 Df000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect
) u+ E" H5 s* {  `% ?' u' x; Cto x
f(4)(x) f four x / the fourth derivative of f with respect to x
1 r0 i7 q/ ]$ ~7 I@f
@x1
# Z8 M0 c8 n' b# `- j" O% Bthe partial (derivative) of f with respect to x1
2 x* H$ a& q9 d  @, v5 X@2f
@x21
the second partial (derivative) of f with respect to x1
+ T5 u( K- E& x$ n, F5 F% p5 n% ]Z
  K; Q! ?2 F$ w$ I( A/ ~1
$ A+ \  H; D# p0 d- v2 I0
0 m/ i/ a8 M( t* [the integral from zero to in&macr;nity
8 Z' \6 V7 H9 p; p5 alim
% G% @- ^) u7 px!0
/ ^2 }/ V/ o$ F5 ]) n+ B6 z% zthe limit as x approaches zero
lim
3 ?" a! l1 r% _  o% Jx!+0
the limit as x approaches zero from above
lim
x!&iexcl;0
the limit as x approaches zero from below
3 [- C( [4 E% R( Y: x4 x+ z" T6 F% _. ~% cloge y log y to the base e / log to the base e of y / natural log (of) y
. }3 a9 j: D/ I0 P7 [4 q% B0 r8 v% oln 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
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
6 o4 P2 M" L4 {, e8 Mbe interpreted as any of: fx, f(x), fx, FX, FX, F&iexcl;&iexcl;X!. The di&reg;erence is usually made clear
5 B, G/ D: v5 e: k# i2 g0 N/ w5 ]3 \by the context; it is only when confusion may occur, or where he/she wishes to emphasise
" L7 s* {! |  ]9 T4 bthe 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.
, m. N7 j  p+ h, E7 o+ y& uSimilarly, a mathematician is unlikely to make any distinction in speech (except sometimes
4 L6 F* P( G% s1 m* q  C3 ^' Ga di&reg;erence in intonation or length of pauses) between pairs such as the following:
- |$ P+ ], ]$ u# s# P& v7 V$ gx + (y + z) and (x + y) + z
, b. Z( e9 W' X) T( V; ?pax + b and pax + b
an &iexcl; 1 and an&iexcl;1
* J- H0 c# ]4 i/ SThe primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science
+ `6 f7 P$ u2 n. j: Land Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have
/ k( P& E+ P; T% cgiven good comments and supplements.
! O8 x1 \% k+ |0 s- k3

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NO常用数学公式

孤寂冷逍遥

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