常用数学公式（符号）读法.pdf

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Pronunciation of mathematical expressions
, V) N, L) {4 {# G+ V0 lThe pronunciations of the most common mathematical expressions are given in the list
) D( J8 Z9 \7 [+ V$ @; mbelow. In general, the shortest versions are preferred (unless greater precision is necessary).
1. Logic
  B7 N" H- t! N) {" U2 V* D9 there exists
: Y! z9 d9 Q; L" ?7 z1 [8 for all
p ) q p implies q / if p, then q
  E7 T; ~# _1 n3 Y/ w( I/ @p , q p if and only if q /p is equivalent to q / p and q are equivalent
. N9 E9 {. z. c1 a0 N& l* }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
A \ B A cap B / A meet B / A intersection B
A [ B A cup B / A join B / A union B
2 V. U6 G, G( ?( lA n B A minus B / the di®erence between A and B
5 e- F! i- F3 j& mA £ B A cross B / the cartesian product of A and B
3. Real numbers
8 E+ j: t2 r+ jx + 1 x plus one
x ¡ 1 x minus one
x § 1 x plus or minus one
xy xy / x multiplied by y
5 \9 w$ ^. \( z$ y' \(x ¡ y)(x + y) x minus y, x plus y
: X' o% E% O; {2 v; Qx
% @$ X$ }2 q# K4 f* R. t" }+ v/ ey
x over y
= the equals sign
0 V; A' t4 s* v- X% sx = 5 x equals 5 / x is equal to 5
x 6= 5 x (is) not equal to 5
+ G1 l4 t6 ?6 T& A# f1
( q! A! k  m% A0 y, Z. F, cx ´ y x is equivalent to (or identical with) y
x 6´ y x is not equivalent to (or identical with) y
4 J8 N: x& L5 M2 A! kx > y x is greater than y
( ~( o9 p7 \0 d2 T6 rx ¸ 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
0 < x < 1 zero is less than x is less than 1
2 u$ {3 z. b5 V2 x. k& Z0 · x · 1 zero is less than or equal to x is less than or equal to 1
3 d" N6 Q0 X+ f8 \& Cjxj mod x / modulus x
; r3 \' ~6 b2 C) j1 C8 Fx2 x squared / x (raised) to the power 2
9 a9 A; a0 G: R# _9 j  px3 x cubed
( L  q( ]" E, U6 m! Tx4 x to the fourth / x to the power four
3 w( D: S# A( Q; t/ Ixn x to the nth / x to the power n
( Q, v& \3 q1 F  Z4 H9 v  n5 Ux&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
0 u$ K# h, z1 A8 O. ^+ @) J9 Wnpx nth root (of) x
(x + y)2 x plus y all squared
&sup3;x
5 r7 Y0 Z5 i7 {1 I) @5 H( ^y
&acute;2
% l, ~3 @% _3 |/ P+ d3 N) Z+ ^x over y all squared
% T( F, a* m$ B* G0 H! S4 Gn! n factorial
$ l6 R/ j7 B  e8 g4 G^x x hat
# ^, a1 }# }+ F- f1 T- R/ c! c5 S&sup1;x x bar
! N. D* x2 ]% ]% N/ R- o+ p~x x tilde
, [+ S9 `$ A  z% z) h  zxi xi / x subscript i / x su±x i / x sub i
/ u0 L+ Z( I$ o# WXn
i=1
3 L1 z/ V4 Q  S5 zai 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
) T2 h- g: b9 o; S% U% d/ D& gOA OA / the length of the segment OA
AT A transpose / the transpose of A
A&iexcl;1 A inverse / the inverse of A
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5. Functions
f(x) fx / f of x / the function f of x
f : S ! T a function f from S to T
x 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
respect to x
, ?; }% k- A4 A! R* }! jf000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect
to x
f(4)(x) f four x / the fourth derivative of f with respect to x
- R4 q" S3 y. R0 C$ ?2 K9 T@f
: }5 V( _2 a. Z@x1
. F9 r  o! \0 N: x, _) k) a2 h/ kthe partial (derivative) of f with respect to x1
@2f
@x21
the second partial (derivative) of f with respect to x1
Z
1
4 h9 ~* E+ X5 h# U0
' }9 `. G& ~% M/ n) @9 Ythe integral from zero to in&macr;nity
1 p/ f1 N7 k( E8 A/ f/ C5 r# olim
x!0
the limit as x approaches zero
lim
" I3 F" ?! w/ T- u6 hx!+0
6 E$ j7 M5 Q- p; ]+ h) _5 p* N$ pthe limit as x approaches zero from above
8 \1 o+ l1 \9 k" Slim
! O$ U# u# c  N9 _6 Y/ _8 H& X& y, jx!&iexcl;0
the 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
$ U4 e8 z3 Z; X- h; x6 Oand in many cases there is no generally accepted \correct" pronunciation.
4 s$ |" m( R4 }7 _- t9 cDistinctions made in writing are often not made explicit in speech; thus the sounds fx may
* T: T! s5 m3 s, R) G+ h7 ube 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
8 z- e' L8 ?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
6 L" C" U. U$ ta 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
+ i. n% Z; a  F4 {- W. eThe primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science
and Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have
given good comments and supplements.
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