常用数学公式（符号）读法.pdf

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Pronunciation of mathematical expressions
" E/ b% h+ @+ q+ @: ^* |1 {# ]  DThe 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
9 there exists
4 _9 I3 ~, U% S/ V. @3 m8 for all
2 D; C* P7 x! n) I; qp ) q p implies q / if p, then q
5 Y5 I  L* h  ^# D1 Hp , q p if and only if q /p is equivalent to q / p and q are equivalent
$ ]0 L( s6 x$ n2. Sets
3 H8 X/ c, P4 h; q# yx 2 A x belongs to A / x is an element (or a member) of A
0 r5 L$ L' O3 F4 D4 Px =2 A x does not belong to A / x is not an element (or a member) of A
; o* Z7 u+ g* l! B+ I0 ?7 f* YA 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
2 L8 w, \2 W  ^* [0 e, X9 CA [ B A cup B / A join B / A union B
A n B A minus B / the di®erence between A and B
2 T+ t2 s9 u, t! b1 ZA £ B A cross B / the cartesian product of A and B
& E6 Z+ K6 H3 l/ t1 H3. Real numbers
/ l+ T, {7 l) v6 i# W" jx + 1 x plus one
% g1 s% P$ R" G) \# hx ¡ 1 x minus one
) k/ F) A  S$ y* K. [# q6 ex § 1 x plus or minus one
* t' x( m: x1 e8 k) J! R& hxy xy / x multiplied by y
(x ¡ y)(x + y) x minus y, x plus y
x
2 |# q4 `6 G8 F+ L+ Ly
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
1
  Q& Q+ I% ]3 N* ]* t0 j; e5 m6 Dx ´ y x is equivalent to (or identical with) y
x 6´ y x is not equivalent to (or identical with) y
7 p( l" ^: ^1 }2 g! L/ H1 Ix > y x is greater than y
x ¸ y x is greater than or equal to y
$ R- `1 g% d7 N' o* O4 u3 \' rx < y x is less than y
' E2 p  K* ?; n4 I7 I" H+ }% Ax · 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
x2 x squared / x (raised) to the power 2
x3 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
( {9 e% \5 ]" C) N6 L7 Ypx (square) root x / the square root of x
0 ^0 H* C' r$ |* Pp3 x cube root (of) x
/ e9 e# }+ g9 _8 e, Up4 x fourth root (of) x
npx nth root (of) x
(x + y)2 x plus y all squared
. h0 ?3 G1 O: o( _4 c&sup3;x
/ u$ F9 {4 t% s  t9 My
&acute;2
4 X  y# l4 F# r6 {! [! E& _& f/ fx over y all squared
0 q/ y, ~  b( @5 o/ pn! n factorial
3 q5 q) s& `' Z7 p4 i2 |' \^x x hat
- m1 s, O. p. r: [8 J. a% t&sup1;x x bar
2 u% R' Q  _" G3 d& G: V# d~x x tilde
$ ^: S/ @" Y/ O0 f) j" Vxi xi / x subscript i / x su±x i / x sub i
/ Z/ t; Y+ ]/ f% Q7 c7 DXn
$ y. x: I" @5 G0 J# ri=1
ai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai
% M: [: [$ M" K( q* j$ H$ y4. Linear algebra
1 [6 k( U. o7 V7 ekxk the norm (or modulus) of x
O&iexcl;&iexcl;!A OA / vector OA
OA OA / the length of the segment OA
2 P7 d. [$ V& B  K* M$ b& pAT A transpose / the transpose of A
% ~4 a3 W0 l9 e  t* kA&iexcl;1 A inverse / the inverse of A
2
+ t/ r+ C3 z. f+ @5. Functions
0 x) y8 I! Z8 G# H/ N% vf(x) fx / f of x / the function f of x
7 s4 ^5 F* K' q/ t1 Gf : S ! T a function f from S to T
' D5 u, F/ a0 C# J8 [x 7! y x maps to y / x is sent (or mapped) to y
2 f: f' ^( N! O( X# G! W7 g# |f0(x) f prime x / f dash x / the (&macr;rst) derivative of f with respect to x
' b% M# |5 _5 U% V; T: [: B3 Lf00(x) f double{prime x / f double{dash x / the second derivative of f with
' U9 w' z3 v, P* L, a& s# [7 hrespect to x
6 T7 s1 r0 z) m; f' a# Of000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect
: ~! X: `6 C- Z0 U: H, U$ |0 F1 Wto x
1 T1 A* D) v% cf(4)(x) f four x / the fourth derivative of f with respect to x
: |9 a# K4 B6 @@f
@x1
3 u( d- P# R0 q0 n5 Y9 Cthe partial (derivative) of f with respect to x1
, ^9 ^" Q) x5 q8 K- N@2f
@x21
2 [* K7 p) x" G' |- Uthe second partial (derivative) of f with respect to x1
; D; B" x+ D  M4 i4 o; PZ
1
0
the integral from zero to in&macr;nity
; m  w$ q: s( e: [' R! {lim
% Z( W6 y0 m! k  {1 H' d4 {x!0
the limit as x approaches zero
lim
4 S8 z  Y# K( d' U( Px!+0
+ L$ ^9 l$ R# G" w; e) l$ v4 Dthe limit as x approaches zero from above
% |- W8 O8 ?$ @7 @lim
9 q* T) K" ?. s7 y) zx!&iexcl;0
the limit as x approaches zero from below
) r0 }% B7 l/ Z% ~loge y log y to the base e / log to the base e of y / natural log (of) y
/ T& \* B2 \7 o9 K# Bln y log y to the base e / log to the base e of y / natural log (of) y
$ X9 x) S- U9 N5 xIndividual mathematicians often have their own way of pronouncing mathematical expressions
7 r3 P1 Z, ?" _; Oand 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
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
& ~) E# N; \9 w9 }2 ?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
& H( d) q7 K0 Y# e7 ]a 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
. Q  N( L) y' f1 V% ~  W  ]an &iexcl; 1 and an&iexcl;1
5 @  @" b. y# w! A& YThe primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science
and Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have
8 \5 |4 ~- s( n9 |& Q! @given good comments and supplements.
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NO常用数学公式

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