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常用数学公式(符号)读法.pdf

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    发表于 2012-1-5 11:26 |只看该作者 |倒序浏览
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    Pronunciation of mathematical expressions) ~- W5 B# A1 I: G
    The pronunciations of the most common mathematical expressions are given in the list
    ; O5 ]- m" Y  ?  I/ Fbelow. In general, the shortest versions are preferred (unless greater precision is necessary).5 m% ]5 R# n4 _- |. L1 U+ V) y
    1. Logic% t+ L+ T) y( }+ d
    9 there exists# W: H2 ~8 k; I$ \1 `7 E, }  Q/ J2 n1 C
    8 for all0 [: y- H% }+ N1 A
    p ) q p implies q / if p, then q* ]) e9 c* E$ F' n( k7 \: c* ^
    p , q p if and only if q /p is equivalent to q / p and q are equivalent9 z" E' [" P2 q! N- ]3 G; Q
    2. Sets
    8 C; e2 n' L6 \6 d+ ?% M& |8 rx 2 A x belongs to A / x is an element (or a member) of A
    " E/ t) i3 @6 @x =2 A x does not belong to A / x is not an element (or a member) of A1 V/ q* o2 {5 r
    A ½ B A is contained in B / A is a subset of B
    $ Q- L4 O- @% Q: J( z' hA ¾ B A contains B / B is a subset of A. K. p- z7 l8 O. m: i5 g
    A \ B A cap B / A meet B / A intersection B6 ]) r! V+ z9 z: L+ @0 A
    A [ B A cup B / A join B / A union B' a: Q: v1 g+ q7 ^9 o* i
    A n B A minus B / the di®erence between A and B
    3 |8 c9 v3 M/ p: qA £ B A cross B / the cartesian product of A and B- i" q4 B" [7 |$ M$ |9 t; v
    3. Real numbers
    7 P' s( z' E4 hx + 1 x plus one
    : ]1 C# B: S* u) \5 K. ?& _x ¡ 1 x minus one
    2 \/ n0 x- W/ G; I$ E# X% H8 {& m" hx § 1 x plus or minus one" }1 R* a6 j* i0 Q
    xy xy / x multiplied by y5 E; y8 d& X1 |# E
    (x ¡ y)(x + y) x minus y, x plus y4 g9 p; j. s' t" M, B: D7 L
    x
    ) ]) Q) a4 f2 d+ H, My3 ^: |5 K4 \  B9 A8 H4 J. ]2 b. D
    x over y
    5 D2 q2 ~, P& Y% j= the equals sign
    , x+ J" f3 m- v. b% Mx = 5 x equals 5 / x is equal to 5
    & ^/ m, L( c2 \% ]) T% Hx 6= 5 x (is) not equal to 5, O  `" a9 W' J3 ^! O/ i. h( }) M
    1
    # V7 Q- T3 t0 Q( ^x ´ y x is equivalent to (or identical with) y
    ; M: @. F6 X+ _* T- a: xx 6´ y x is not equivalent to (or identical with) y
    * \6 ?) u' u( y% L+ gx > y x is greater than y
    1 S2 Q% Q* S2 g# }- x# i3 mx ¸ y x is greater than or equal to y: Z9 ?* P( |% M9 J& ]: K
    x < y x is less than y
    9 Q# ^. G1 K8 {- C- i# nx · y x is less than or equal to y3 b. v; y% P2 p# K8 L
    0 < x < 1 zero is less than x is less than 1( I. Y+ ]& d  t3 s# B
    0 · x · 1 zero is less than or equal to x is less than or equal to 1
    0 ]5 q( h$ `0 j/ E7 U9 p. j4 ajxj mod x / modulus x
    $ Y! ~: U; w9 Hx2 x squared / x (raised) to the power 21 \9 ?* v4 P3 P; w
    x3 x cubed
    # e5 h1 Q& O4 B2 |. Cx4 x to the fourth / x to the power four
    . _# t( l- \! ~  Lxn x to the nth / x to the power n
    $ @  [" R& d; a8 m# g- K2 rx&iexcl;n x to the (power) minus n( q  Q' _) A) K0 Y4 L
    px (square) root x / the square root of x
    ) z" Y2 M! s3 S; h- v, T) Bp3 x cube root (of) x4 c! m4 R6 g- T9 Y
    p4 x fourth root (of) x) J3 A9 V/ B$ x4 A" a
    npx nth root (of) x
    , d, Z* c2 g: C) p% j9 }( l& D(x + y)2 x plus y all squared. e- B0 d" Z. G# Z9 o. F- X+ C0 v
    &sup3;x  z4 E6 N9 t# w, V
    y
    " A, K6 V) n& O0 p) A3 S" i& U&acute;23 H# |& l* I* z# l5 _
    x over y all squared0 I; y2 w& h; v: t4 M- V6 m
    n! n factorial9 w6 @7 c: U. w0 O6 i
    ^x x hat
    3 @% A, z  c0 V% C7 j&sup1;x x bar( N- F5 D1 L4 U2 t1 V5 v& ~
    ~x x tilde
    : n0 t: s. E4 O! L& {xi xi / x subscript i / x su±x i / x sub i
    ' @/ j& p" s+ u' T& |0 _Xn* e( x. f. G3 }' F; _7 T0 A4 g+ G
    i=1
    + X% g1 \- |3 c7 Cai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai4 Q' @) Y1 q: o& o' F9 B
    4. Linear algebra! z3 v5 a# ^+ y7 @  Z" f* s/ x3 v
    kxk the norm (or modulus) of x
    1 Q5 J+ L/ o, F1 S3 b) g$ e& QO&iexcl;&iexcl;!A OA / vector OA
    2 @+ M! i6 `7 s) eOA OA / the length of the segment OA
    # {, R% c+ q6 W2 E' X6 ^AT A transpose / the transpose of A
    ! _) R5 n5 `+ bA&iexcl;1 A inverse / the inverse of A0 u: b$ \+ |3 ]
    2+ H( y3 @5 F# P& {- K
    5. Functions: H0 ^7 q, ]/ K/ ~- ?' X
    f(x) fx / f of x / the function f of x
    , N" o# K. v& G$ _f : S ! T a function f from S to T3 w3 A5 ]/ d/ E! V
    x 7! y x maps to y / x is sent (or mapped) to y. @" ]1 J- b. X- R8 @8 R& B
    f0(x) f prime x / f dash x / the (&macr;rst) derivative of f with respect to x
    5 Y# g2 g! C# o8 e$ I4 N! Xf00(x) f double{prime x / f double{dash x / the second derivative of f with7 c0 ^1 t2 ~7 L9 w+ F
    respect to x
    1 b& ^7 L3 W6 wf000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect/ X& p8 l; g9 d) Z7 [/ \* L9 L
    to x* q+ }% a, t0 |+ \
    f(4)(x) f four x / the fourth derivative of f with respect to x
    ; b8 o, p% N' o@f, v! b7 \7 y8 q1 I
    @x1, J3 t7 t/ p+ |+ c& ~& @
    the partial (derivative) of f with respect to x1
    4 @7 a. g- S$ J& T@2f
    . i) v6 |1 O+ u" ?* Q& w9 R+ f! @@x212 j7 }/ o4 D  }( s" ?
    the second partial (derivative) of f with respect to x1
    ) l! S) x3 p# b: e5 zZ/ O  K3 s) y% D
    1
    , I5 L# Y; F4 ]. R4 T0
    ! @0 c. d+ f- y& k  O" }5 Z. Sthe integral from zero to in&macr;nity
    4 [; ]8 J5 ~: z" ~2 U6 i5 Wlim% j  }0 q% y: I. [# I) |& t
    x!0
    8 R1 p- i, y: k' s. q6 q# Nthe limit as x approaches zero
    7 g% {/ Y' v- s. z4 ?lim
    4 C0 \6 d  |4 B" w6 _x!+0$ `- P- C( @! N2 k$ C! B
    the limit as x approaches zero from above
    * i  ~7 A# R+ d- W+ ^lim, j( |' ]5 ]! E% x/ a
    x!&iexcl;0
    # N) ^$ g. V) ]' }! i3 Jthe limit as x approaches zero from below
    / S/ i$ a! _  l- Zloge y log y to the base e / log to the base e of y / natural log (of) y
    : E+ H4 G% T* x3 f% {7 Z( Rln y log y to the base e / log to the base e of y / natural log (of) y* N+ L/ t2 c, S/ G7 v' N4 ~1 F7 W
    Individual mathematicians often have their own way of pronouncing mathematical expressions$ d3 s8 N! w3 Y- z$ M3 @; k2 `" ?3 a+ p
    and in many cases there is no generally accepted \correct" pronunciation.
    2 C: F6 T6 U! z. r1 g7 ZDistinctions made in writing are often not made explicit in speech; thus the sounds fx may9 h+ D5 J2 |( j: A8 C
    be interpreted as any of: fx, f(x), fx, FX, FX, F&iexcl;&iexcl;X!. The di&reg;erence is usually made clear
    ) }% ?/ t4 g# ^, X/ u! }by the context; it is only when confusion may occur, or where he/she wishes to emphasise3 {! `% d8 ~9 H
    the point, that the mathematician will use the longer forms: f multiplied by x, the function' M3 j6 ]1 |& H: ]; Z! d# s
    f of x, f subscript x, line FX, the length of the segment FX, vector FX.
    5 o4 R/ m, w7 J: _- J6 ^2 L7 eSimilarly, a mathematician is unlikely to make any distinction in speech (except sometimes  L' h% c; z$ B, j9 Z( t) j, }* c
    a di&reg;erence in intonation or length of pauses) between pairs such as the following:7 I( H+ I7 `. ]. i& p9 S1 a
    x + (y + z) and (x + y) + z6 A. e2 n/ C) o/ T5 ]4 n
    pax + b and pax + b
    % z' n. V9 I$ nan &iexcl; 1 and an&iexcl;1
    7 R! o, r1 M# S2 dThe primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science
    $ v" g$ N: J, L0 jand Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have( U0 T- h$ G" Y2 f- T
    given good comments and supplements.# j2 f+ A8 V* M! h) m+ ?
    3

    常用数学公式(符号)读法.pdf

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