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 ! s- D, f8 @( `( O6 G. x3 xThe pronunciations of the most common mathematical expressions are given in the list# s+ o' B; a& a; X/ f# S& D
below. In general, the shortest versions are preferred (unless greater precision is necessary). ' @" s: L r4 J( B6 q; X; l1. Logic' Z" n2 I1 e$ C1 S3 V
9 there exists $ H3 E4 R6 v3 W9 Z7 L8 for all " n2 y2 e0 g0 t3 rp ) q p implies q / if p, then q4 h, @5 t0 C3 u3 d5 G
p , q p if and only if q /p is equivalent to q / p and q are equivalent X( r# N+ H: i8 z2. Sets0 v, D2 E; G8 A& K9 Y- L
x 2 A x belongs to A / x is an element (or a member) of A 1 ?$ O% l3 m5 s `$ B0 Gx =2 A x does not belong to A / x is not an element (or a member) of A% J* D7 I& ^1 k C' u' S
A ½ B A is contained in B / A is a subset of B- D' p% b8 o7 Y o7 T7 [" d
A ¾ B A contains B / B is a subset of A 9 @- F8 Y: j7 ]! H9 i9 p) JA \ B A cap B / A meet B / A intersection B $ [+ M* T2 n% s) r' ?4 fA [ B A cup B / A join B / A union B 1 f1 b. i3 x4 @. v( |2 p X/ c0 RA n B A minus B / the di®erence between A and B - h: x( ?# ?' dA £ B A cross B / the cartesian product of A and B- ]' Q( l+ o* d
3. Real numbers' j' e* f& H' O/ d$ b
x + 1 x plus one {) c8 P# i- ^1 `) {$ j+ l4 E, L/ K4 fx ¡ 1 x minus one 4 l; K! E; U# wx § 1 x plus or minus one1 N* q6 C8 o" R7 c! T0 E4 q% h/ t
xy xy / x multiplied by y0 x+ @2 Y: |6 t2 W3 E
(x ¡ y)(x + y) x minus y, x plus y , L4 x0 k) @0 A" Ax2 ^! _3 k7 H+ |
y# @, \3 d9 D/ }$ F- v
x over y6 x3 j) w$ d$ L9 f
= the equals sign6 y+ j3 w! k9 |, Y7 `# q
x = 5 x equals 5 / x is equal to 5 " x4 p! d; ^) R' \x 6= 5 x (is) not equal to 5 9 q$ X- E- B% _1 Z1 ; b7 ]; {7 k( l1 W9 M& P* Px ´ y x is equivalent to (or identical with) y$ v& p1 e( F+ [0 T3 ]
x 6´ y x is not equivalent to (or identical with) y( z4 ?" A, D p! c
x > y x is greater than y t" X9 {" z$ T) T7 |
x ¸ y x is greater than or equal to y" J* Q; y$ `- x5 K5 ?
x < y x is less than y 7 I. v6 \9 I/ {# k* {x · y x is less than or equal to y! J' _9 X1 B7 U: i2 }$ z% q* r
0 < x < 1 zero is less than x is less than 1 ' G+ n6 F* Y4 _8 o. R- y# i0 · x · 1 zero is less than or equal to x is less than or equal to 15 r# I2 v) a0 n1 U% [$ y* g
jxj mod x / modulus x ( p1 d# @ Y' A) Kx2 x squared / x (raised) to the power 2 0 A$ X' \# h* J2 ~5 @: Xx3 x cubed$ ]1 R. T& M' s
x4 x to the fourth / x to the power four ' I* E( K% g; r0 P t6 e% Sxn x to the nth / x to the power n ) @! x/ v9 @2 ~$ l1 }x¡n x to the (power) minus n: d& n/ F0 Y& |6 g, O! F: Y& o
px (square) root x / the square root of x1 z0 N4 g- L3 }3 t
p3 x cube root (of) x# N' I" s0 p6 D; | |. I. G) |- f
p4 x fourth root (of) x ) g7 H/ F/ Y/ A4 j+ s# vnpx nth root (of) x, K- ^6 p2 S {! g! M8 e6 H, e
(x + y)2 x plus y all squared 1 i* [" `: X* @5 Z8 S% U³x, V# U9 }/ E4 ]6 n. ?# }6 d
y; h1 J4 s1 w( u* L$ E( j; h
´2 . q1 k& \# _. t( z7 N$ p, N- N2 Cx over y all squared# @. T( }& v! T% `: U7 p$ A5 Q
n! n factorial - R1 t$ B5 }! y; v& y& T. I. S& M^x x hat, a1 U6 k D. {* q" n ~: U
¹x x bar ) C3 G+ \4 @2 a& S- a6 R8 n~x x tilde8 ]) e! \, h/ a5 m% _
xi xi / x subscript i / x su±x i / x sub i4 W$ s% m) l _* e7 Y
Xn$ Y; W) V8 b) ^: S( ]- V3 t
i=1: n& b* Q, U/ I; X5 L. e
ai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai* Q0 Y$ P4 `7 x2 L
4. Linear algebra0 I! Q8 `, B2 q( G
kxk the norm (or modulus) of x- M) ^+ s8 h l
O¡¡!A OA / vector OA + `3 c$ @/ U y' TOA OA / the length of the segment OA " s8 U- h/ ]- e b# n% mAT A transpose / the transpose of A 1 M. H! ?' r2 @2 aA¡1 A inverse / the inverse of A " h6 N* _# }! R5 ^5 v8 f2 7 b$ X8 k7 ?* J& {. Z$ P( c5. Functions/ D# ]6 A a) d$ I7 P
f(x) fx / f of x / the function f of x # o$ Z% @" S- D4 t, w5 D5 R; mf : S ! T a function f from S to T + d' Y9 A. s5 P% q2 [3 xx 7! y x maps to y / x is sent (or mapped) to y) z- b( ], D6 k; f& M
f0(x) f prime x / f dash x / the (¯rst) derivative of f with respect to x+ U2 i$ k, w3 |6 X. E, L
f00(x) f double{prime x / f double{dash x / the second derivative of f with$ A) F9 v3 @$ O2 E
respect to x# }. [' J$ {# ~; t- G1 w; T9 J- z
f000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect/ ~2 e" q8 ~, F* o7 S. s! ~
to x, s/ d5 O6 y; C! E. o0 ]
f(4)(x) f four x / the fourth derivative of f with respect to x 6 e% o" m( P a1 o; e8 f@f# G2 `# i+ B- g
@x1 1 T; s! ]& _, G6 M7 lthe partial (derivative) of f with respect to x18 S7 [ T; F* c: c" ?
@2f. K2 h- F+ o; a) D
@x21* U! s9 v. ?3 G Y* P* {0 Q5 |' y
the second partial (derivative) of f with respect to x1 4 E( D& O6 x) J/ Z3 p* C/ h2 |Z 2 y& K3 ~ a7 G3 @# W# a1) ]4 c% T& p, \; ?
0 9 }2 R" Q# U% D1 Athe integral from zero to in¯nity6 G2 Y6 n2 C. O( N8 D9 G7 V
lim2 Z" R$ @+ p4 _2 o1 o# F
x!06 ~ [' g. I" _. n; V. X$ l
the limit as x approaches zero4 Q/ R5 k5 D; o; h" S
lim , ]2 o$ t( |$ ^+ kx!+0+ D, G1 l/ m, _1 _1 R" H: T; P
the limit as x approaches zero from above( B" j2 T N6 H
lim 5 a* u ^8 e1 o% L1 l. Qx!¡0 : E9 u( e$ U3 h$ s, B6 c) f6 sthe limit as x approaches zero from below 0 v3 M) [! t3 Q6 h( R9 Tloge y log y to the base e / log to the base e of y / natural log (of) y8 v" ~4 f+ \; P- P! x) s
ln y log y to the base e / log to the base e of y / natural log (of) y , n% W. j3 D! s" o1 J1 RIndividual mathematicians often have their own way of pronouncing mathematical expressions& i- s/ @" x e- u6 n7 C
and in many cases there is no generally accepted \correct" pronunciation. " q: d% O+ `/ u$ sDistinctions made in writing are often not made explicit in speech; thus the sounds fx may % B1 @: O9 M# W7 i) G5 ]be interpreted as any of: fx, f(x), fx, FX, FX, F¡¡X!. The di®erence is usually made clear4 ?9 O9 I. s% E' j0 l2 C! y. g3 o5 r
by the context; it is only when confusion may occur, or where he/she wishes to emphasise 1 q! y" c, O$ b& p/ lthe point, that the mathematician will use the longer forms: f multiplied by x, the function 1 e) P4 q5 L+ }1 H6 Df of x, f subscript x, line FX, the length of the segment FX, vector FX. / X `# }3 l$ oSimilarly, a mathematician is unlikely to make any distinction in speech (except sometimes5 Y8 ?- N8 W& E" p6 `
a di®erence in intonation or length of pauses) between pairs such as the following: ; x# U$ x. s& c7 g9 _4 `9 gx + (y + z) and (x + y) + z : O) O2 Q+ N" [3 mpax + b and pax + b( M f5 m9 U- B/ `2 p0 b
an ¡ 1 and an¡1 # [( }' v, r j {. S2 g+ wThe primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science & c+ y( f- z S. p. R% rand Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have% X1 R8 H! N: e+ E# W# s
given good comments and supplements.% ?2 N8 }6 A. ?
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