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).
* g# P, o; s  o) v/ o# E1. Logic
9 there exists
8 l" f/ X9 s) N# |0 Q0 S4 B8 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
8 w7 I$ a5 t" e- HA 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
, Z: B8 |) o, t, RA n B A minus B / the di®erence between A and B
( E. i! J( n5 l. X: U/ [A £ B A cross B / the cartesian product of A and B
3. Real numbers
x + 1 x plus one
x ¡ 1 x minus one
x § 1 x plus or minus one
! O8 r( Z3 ~, a3 |" Z% P6 G6 Txy xy / x multiplied by y
8 i8 t8 V- T6 ^& R(x ¡ y)(x + y) x minus y, x plus y
x
y
x over y
= the equals sign
$ G8 v6 ~" n8 v/ C2 p  C. |x = 5 x equals 5 / x is equal to 5
& c) @/ H! I- V$ ex 6= 5 x (is) not equal to 5
' \" l) x0 K5 t& S3 u3 ^" N/ i1
4 D2 G2 b2 p2 D4 b) ^- Z1 _+ Sx ´ y x is equivalent to (or identical with) y
x 6´ y x is not equivalent to (or identical with) y
! o7 V5 N8 Q6 J6 Q& X! q* Qx > y x is greater than y
x ¸ y x is greater than or equal to y
x < y x is less than y
- K5 V% U0 r6 q, L7 K( Lx · y x is less than or equal to y
0 < x < 1 zero is less than x is less than 1
3 f/ j. h0 O$ L0 · x · 1 zero is less than or equal to x is less than or equal to 1
5 A+ n9 p: P$ jjxj mod x / modulus x
/ q) m* H: B: q5 f: P! g% G3 Y5 Ox2 x squared / x (raised) to the power 2
x3 x cubed
8 e+ a* ~$ S- q( a8 Vx4 x to the fourth / x to the power four
  m# k" J" X( E% V% |- Wxn 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
5 P: {+ ^4 O" v: G7 i* \9 C5 r6 dp3 x cube root (of) x
. Q5 j# e; B$ M0 jp4 x fourth root (of) x
4 S2 q- o8 [& I. a5 H. d' Fnpx nth root (of) x
$ |' D5 l% @: W* y  }1 z+ n1 ?(x + y)2 x plus y all squared
* @0 Y$ J# p! o' m&sup3;x
y
, K9 ~7 a9 f6 c5 T5 s- D&acute;2
x over y all squared
7 z$ Z: P/ ?  T: G. F9 n: cn! n factorial
^x x hat
&sup1;x x bar
~x x tilde
- C: e" ], ?3 |- ~. M: axi xi / x subscript i / x su±x i / x sub i
- v2 ^( K4 }3 ^  c2 RXn
i=1
" d+ c% o" J: @; d$ K% r# aai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai
$ S# y. n: F9 i- M6 {4. Linear algebra
kxk the norm (or modulus) of x
O&iexcl;&iexcl;!A OA / vector OA
OA OA / the length of the segment OA
. w+ K9 i* _" ]7 ?. `( {3 FAT A transpose / the transpose of A
( ~$ G0 V. V+ e  Q) e( r; f2 V( IA&iexcl;1 A inverse / the inverse of A
6 I) S/ i% P& N1 j; _2
4 X8 C3 L: B: R3 H3 [* }5. Functions
' Q5 ~9 }) r  D% @$ g0 sf(x) fx / f of x / the function f of x
, G  ]8 ?; e% B4 S: t1 nf : S ! T a function f from S to T
  y9 b5 ~  \# C  R& O0 J0 ~, Fx 7! y x maps to y / x is sent (or mapped) to y
; u7 q# f2 s( V  q* _- of0(x) f prime x / f dash x / the (&macr;rst) derivative of f with respect to x
6 s! m8 S1 U- ~0 {6 G; Hf00(x) f double{prime x / f double{dash x / the second derivative of f with
0 T6 u" A: V( l; x* Nrespect to x
f000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect
+ d  C- b5 |5 l+ pto x
f(4)(x) f four x / the fourth derivative of f with respect to x
@f
@x1
  q5 X1 ]1 y, y+ a! rthe partial (derivative) of f with respect to x1
; m& F/ d6 t- L/ J6 V8 ^8 B0 P@2f
# k, v, n* R2 [+ L@x21
7 ?7 V: z& U) L. ^the second partial (derivative) of f with respect to x1
Z
' |; @' h( K% l4 H5 G+ b$ g& e1
; ^$ S8 |- U" ^: z3 {0
the integral from zero to in&macr;nity
9 a% @4 u$ V; j4 ]7 nlim
9 W4 [. R2 G; Ox!0
0 L6 N) z; s! t: q# |" ^6 Vthe limit as x approaches zero
9 ^! X4 T9 H& B0 @lim
4 A4 o& \5 r" w) y/ a9 H; [x!+0
the limit as x approaches zero from above
lim
% y/ L* T5 s) I. lx!&iexcl;0
6 f+ x/ U6 d0 L" ythe 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
+ O# g( e7 T+ E6 v4 S4 d( Dand 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
+ x" P, U( ~) N% g; ?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
3 [. f' f* w% k7 M8 `7 j$ zthe 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.
/ {* X; y+ y9 O8 z9 t" J  t+ SSimilarly, a mathematician is unlikely to make any distinction in speech (except sometimes
a di&reg;erence in intonation or length of pauses) between pairs such as the following:
x + (y + z) and (x + y) + z
. N, i; p; Q% v, @4 hpax + b and pax + b
# o* Z! J+ P* e, |5 ]3 gan &iexcl; 1 and an&iexcl;1
9 G" V2 \, X: ?( b+ GThe primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science
1 P9 v5 N7 p6 O. L/ d0 land Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have
5 G  K4 b: ?5 ^$ k' v% @given good comments and supplements.
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NO常用数学公式

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