标题: 常用数学公式(符号)读法.pdf [打印本页] 作者: lilianjie 时间: 2012-1-5 11:26 标题: 常用数学公式(符号)读法.pdf Pronunciation of mathematical expressions & ~, L$ J1 x4 Q! Z7 K/ dThe pronunciations of the most common mathematical expressions are given in the list " o. w. `6 A( o# U) d/ s. pbelow. In general, the shortest versions are preferred (unless greater precision is necessary). ; _) D1 m; U: v3 }1. Logic2 k! c1 e4 p& T5 `6 S
9 there exists a& ], i9 b* K" N% n; D. N1 F* y8 for all , m- @( A# I2 G, w1 c+ f! ap ) q p implies q / if p, then q* D/ B& n! l& b$ ?/ g' @# |
p , q p if and only if q /p is equivalent to q / p and q are equivalent ! k' h- J# V( ?( r+ \8 J4 b2. Sets ; d# T, O) V3 u& `& nx 2 A x belongs to A / x is an element (or a member) of A# _, L P T7 Z& l8 s" _* l) Q
x =2 A x does not belong to A / x is not an element (or a member) of A 6 l8 I+ c+ {1 ]A ½ B A is contained in B / A is a subset of B2 f- Y2 C. ^, g: z2 C \% [( C) S0 b
A ¾ B A contains B / B is a subset of A : Y7 E5 ?( c, G$ A# p* GA \ B A cap B / A meet B / A intersection B, \6 n- T4 ^6 J. I
A [ B A cup B / A join B / A union B3 T; w5 B* r3 @8 `
A n B A minus B / the di®erence between A and B0 J- X) T5 J- p2 w; T
A £ B A cross B / the cartesian product of A and B ' x2 r; H9 {: p+ {0 [# d9 n3. Real numbers; K) W! H; @# \* u# h z. x* p' N
x + 1 x plus one* i# V7 F) f4 e. c) M& y" v
x ¡ 1 x minus one 5 Y) F7 A8 x4 Wx § 1 x plus or minus one$ L. G2 F- e. [+ U. X& o
xy xy / x multiplied by y3 d+ f$ T; {3 W; t1 z& t
(x ¡ y)(x + y) x minus y, x plus y 1 x5 \% A! D/ F7 G/ H/ L2 Px& M( \. X# z/ G2 Q) P* V
y / s: J3 Q# u4 r# jx over y 4 t- f6 E- r7 d7 ?" b, c% X= the equals sign$ i; q7 b$ O/ p: M) R! S2 q6 Z
x = 5 x equals 5 / x is equal to 5 + Z9 {* V. J: i+ B$ W0 j* Dx 6= 5 x (is) not equal to 5- J) i' p& }' y: Y
1 - D. X0 ?# N% u, [x ´ y x is equivalent to (or identical with) y8 q) V* y' G2 ?; `" g
x 6´ y x is not equivalent to (or identical with) y/ F" i0 s0 b: S; R1 y% \
x > y x is greater than y $ k$ o/ a! i4 z/ o% ?( v( s) rx ¸ y x is greater than or equal to y 4 S# J, b0 w2 m+ Tx < y x is less than y 5 H# S: T, O I# S" b& mx · y x is less than or equal to y . G. X% }( X7 o/ ~7 n. V" m0 < x < 1 zero is less than x is less than 19 q- }- Q1 G5 u; P6 q2 n: s+ }6 R
0 · x · 1 zero is less than or equal to x is less than or equal to 1 1 J9 F# q. M q9 k- p' Kjxj mod x / modulus x 6 J' h- }9 {4 ox2 x squared / x (raised) to the power 2& n# g6 N' J2 J s) ]
x3 x cubed 9 j1 ^$ v0 Z2 j# k! V4 z5 ox4 x to the fourth / x to the power four3 S8 }$ a/ x! @/ @9 w$ Q
xn x to the nth / x to the power n 3 B2 J$ U$ \2 D% r2 K, O; `x¡n x to the (power) minus n, ~0 @3 S" x. V$ G4 Z
px (square) root x / the square root of x n9 |. O$ O2 d
p3 x cube root (of) x * }$ Q, C/ z+ L/ op4 x fourth root (of) x 0 f8 K( S9 h; Q) _% {( hnpx nth root (of) x 9 |/ \( ^$ d" i6 z7 y(x + y)2 x plus y all squared# o, O4 y+ ?, `/ e B: `4 E
³x( e7 S* J3 |3 V
y " w) Q4 i% ^: c# M' B4 ~% D´2' A; w- J6 c; X! }7 `$ W: K% y
x over y all squared . p! `5 ~4 c5 [5 F) A9 Sn! n factorial! w0 E I: ]* S9 ?- |0 D$ Y' v
^x x hat $ U7 T! S( J8 D$ {+ ^5 \¹x x bar ) l- D, i! ~+ w2 \. g: b~x x tilde % [3 W2 V# t. A3 exi xi / x subscript i / x su±x i / x sub i* `$ N' N; O2 h) _8 `
Xn 1 A+ ]9 k5 G! ?- Y6 u) T: @i=1 ; u& ]1 V: K- ?% |( ]- D! Lai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai 7 m, c4 ]1 t+ c$ G* _* J5 I7 v4. Linear algebra - ^: M8 Y( Y6 K4 i# s! T" }0 Bkxk the norm (or modulus) of x- F& w4 j: ~8 l9 r/ f5 R; b
O¡¡!A OA / vector OA & }/ J8 ~, w* Y: e3 EOA OA / the length of the segment OA & Y- i3 m* Z2 f8 HAT A transpose / the transpose of A - N C' ]4 s/ y: ~A¡1 A inverse / the inverse of A & c( n6 H' D2 F0 r; h* U2 m2+ s6 K$ J2 O' G
5. Functions 3 a& {. F% Q8 D, B' Sf(x) fx / f of x / the function f of x 0 L( X( l6 |+ p8 Kf : S ! T a function f from S to T) [% r v" h8 P7 n- ~) P, g2 y
x 7! y x maps to y / x is sent (or mapped) to y. @3 d" i' [' i
f0(x) f prime x / f dash x / the (¯rst) derivative of f with respect to x) f- H8 K' F7 s( m% U
f00(x) f double{prime x / f double{dash x / the second derivative of f with2 u( Z1 I4 {" K: w' y) h& ]
respect to x; z" H' L5 r+ E1 W1 e/ p: j' u
f000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect 5 V, f2 f6 W4 W# W" r* \- N' p5 o* k% Jto x ( ~1 w- ], I' b/ Of(4)(x) f four x / the fourth derivative of f with respect to x9 f/ o6 r+ b- W
@f 6 E8 p+ K# M4 ^ |% ~) p/ Z@x1 1 L. d# G9 h& D/ Uthe partial (derivative) of f with respect to x1 / u. V7 n4 S7 \! ?1 P8 e2 l@2f* l! I2 F, I4 e: F% P- \
@x21 : T' I4 ?: ~$ x4 D+ X0 I8 @the second partial (derivative) of f with respect to x1 ' H/ t, _( o/ I6 c) i* a! IZ ' f( G8 ^% z5 z% q1 9 K! ~' x: X; j! P0 ' p% ^% J! a1 U0 h6 {# Gthe integral from zero to in¯nity F. l0 K9 q3 P! E) G% Wlim( ]8 w3 n, {6 Y
x!08 c6 F7 F8 O, P# y, d6 ^0 s$ K
the limit as x approaches zero# J3 W- n* c1 U5 d" v/ A
lim ' C" F- q+ D/ z% Ox!+0 2 H! n6 V: ]6 O4 a# R3 L6 z. U, ^the limit as x approaches zero from above . p* j$ R) N8 h* xlim / u0 R5 C4 J$ X; S' `6 q4 [x!¡04 M/ ?, c/ z" Z/ }" q5 v/ F* B
the limit as x approaches zero from below 6 l/ @: r+ j g3 J9 O- Wloge y log y to the base e / log to the base e of y / natural log (of) y ; \( T# ~. _ j8 a, e1 B# j, k6 u0 Eln y log y to the base e / log to the base e of y / natural log (of) y : j. c3 i; }2 n9 b5 P; KIndividual mathematicians often have their own way of pronouncing mathematical expressions / i# F7 ^8 a$ V1 @, ~2 Aand in many cases there is no generally accepted \correct" pronunciation.6 m3 q( I4 K* T" f$ m. d U
Distinctions made in writing are often not made explicit in speech; thus the sounds fx may : j5 c8 P, k4 Y9 } i' V# Kbe interpreted as any of: fx, f(x), fx, FX, FX, F¡¡X!. The di®erence is usually made clear ' H# x! }: c5 u. uby the context; it is only when confusion may occur, or where he/she wishes to emphasise( I9 J) [% p0 |' h9 W! i+ n# d
the point, that the mathematician will use the longer forms: f multiplied by x, the function+ R+ q6 ^5 ^' E4 C1 ^
f of x, f subscript x, line FX, the length of the segment FX, vector FX. # S! A7 d: e S: I* N. N3 lSimilarly, a mathematician is unlikely to make any distinction in speech (except sometimes * c. L, `! f6 s0 b5 ra di®erence in intonation or length of pauses) between pairs such as the following: 7 C* G9 U( K+ B2 X# I0 vx + (y + z) and (x + y) + z " ^) q0 d& V5 _1 _( n0 e) npax + b and pax + b/ ?4 N. u; G6 Y" r
an ¡ 1 and an¡14 Q' I& }4 \' a
The primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science1 f$ \6 A0 p8 E5 b+ U
and Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have 0 n" U- S2 U+ S" i+ Zgiven good comments and supplements.. F! Z9 T& T7 B) w n, M, h8 [# [! x6 L
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