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常用数学公式(符号)读法.pdf

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    Pronunciation of mathematical expressions
    $ Q" ?/ X* F! i8 V9 n3 `The pronunciations of the most common mathematical expressions are given in the list7 ]( z5 `/ E7 n6 j$ m
    below. In general, the shortest versions are preferred (unless greater precision is necessary).9 @0 j) D% Z8 z+ e4 j- Y
    1. Logic
    9 H; U8 j! v. j; f2 u; a$ i9 there exists
    6 Y/ w2 N5 A5 N/ V8 M6 `8 for all
    + v$ q  i- B9 M" G' Zp ) q p implies q / if p, then q' t0 k) @" Z1 n% _3 ]
    p , q p if and only if q /p is equivalent to q / p and q are equivalent
    , ?$ d- z. Z: X2. Sets
    9 @4 y+ f1 n1 _3 Q6 p* Qx 2 A x belongs to A / x is an element (or a member) of A/ j; K4 _1 n3 `6 w5 `" e
    x =2 A x does not belong to A / x is not an element (or a member) of A
    0 h: d2 O) L% V3 qA ½ B A is contained in B / A is a subset of B
    2 @, l% c- H2 N) [/ i* }( w1 kA ¾ B A contains B / B is a subset of A  z' |3 ^5 c9 \0 r9 v
    A \ B A cap B / A meet B / A intersection B' s- I( A1 U" d
    A [ B A cup B / A join B / A union B
    ! C: o2 k0 q, E% t8 p: x! t9 \A n B A minus B / the di®erence between A and B
    ' \: v/ E1 R2 h/ w. UA £ B A cross B / the cartesian product of A and B
    0 C/ ]. [% c  X% r6 d: A, }3. Real numbers
    6 F9 O9 e: C; Q0 r& v6 P3 wx + 1 x plus one. P; Z4 |0 l& ?: x. v
    x ¡ 1 x minus one! P3 I2 f2 A" b) R0 _/ F
    x § 1 x plus or minus one! @8 T/ \; B' i
    xy xy / x multiplied by y
    3 S9 g, q1 k1 o(x ¡ y)(x + y) x minus y, x plus y
    0 B) i( q# x5 T( }4 P. q2 ~x
    4 P( s3 J3 z. t! fy
    $ Q# T: C$ ?' Xx over y+ T- Q8 c. W/ S8 j" R, ~, C
    = the equals sign: p! e# P/ J4 _& |' o: v' _( h
    x = 5 x equals 5 / x is equal to 5# y" ?0 }) a3 Q8 @
    x 6= 5 x (is) not equal to 5% L) c! O7 a8 ?: Z/ J
    1( \) r7 D( E/ R0 X9 ?
    x ´ y x is equivalent to (or identical with) y2 W* |6 |: p+ a
    x 6´ y x is not equivalent to (or identical with) y
    $ J: y$ O  [6 J$ X: Vx > y x is greater than y
    # t3 q4 w7 x- Y- q3 n7 x3 [x ¸ y x is greater than or equal to y
    4 n: ^2 C1 g! c. H/ A# mx < y x is less than y+ z: h6 D0 m2 C. m% R/ @+ \, O3 M
    x · y x is less than or equal to y* s' h8 T8 v8 U2 V9 v& D- k
    0 < x < 1 zero is less than x is less than 1
    - h1 V( \  ^( |* q" t3 c& ~/ Q" n. r0 · x · 1 zero is less than or equal to x is less than or equal to 1
    8 x3 Q; Z; G! M+ N; q) l5 cjxj mod x / modulus x
    ( E! p+ a$ c" P1 L+ {; h5 wx2 x squared / x (raised) to the power 2
    ) Z3 v+ o$ o1 L/ [& D7 r4 n% jx3 x cubed( v9 f- [7 J* V5 v, ^" L5 \9 k) c
    x4 x to the fourth / x to the power four
    3 _2 D7 f: O5 k( s. @  Rxn x to the nth / x to the power n
    " H2 Z3 v. ?. V3 i# Z1 O5 W, Sx&iexcl;n x to the (power) minus n
    + L# v3 R4 e2 J% _: P0 @$ fpx (square) root x / the square root of x  Y! Y( F1 e  V
    p3 x cube root (of) x+ a' B. J/ F2 Q4 [: C7 P
    p4 x fourth root (of) x
    7 X' |. b8 w& Q, [" P( ?npx nth root (of) x, `$ o, O8 N$ ]- b
    (x + y)2 x plus y all squared8 G5 Q. ^. @  [7 x1 M/ w
    &sup3;x
    ' K0 }. b/ C1 K2 w5 p3 Hy  A& M7 s9 v/ c$ t0 C
    &acute;2
    0 @% ~5 \. W2 q5 ex over y all squared$ g7 Q+ W" Y! ~- \& }; U3 p
    n! n factorial( Z( \) p* ]% b. x& k! x$ [
    ^x x hat% \7 K3 S4 d" R! u! M
    &sup1;x x bar7 i& }/ ]7 w6 ^. |; _& _8 B  j
    ~x x tilde1 n: a3 ~4 V) \& u
    xi xi / x subscript i / x su±x i / x sub i: A+ N$ Y0 K4 X" J5 G. T& p
    Xn% N9 K2 B8 x3 E7 \  Y- |5 P8 _
    i=11 r9 T( }- _% u5 H" S1 b
    ai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai
    , E( e9 W; d$ K, l4. Linear algebra0 [0 u. ^4 E% E2 L
    kxk the norm (or modulus) of x5 W- r. \/ }; Q5 L3 l& f' H
    O&iexcl;&iexcl;!A OA / vector OA' K) h4 m' c5 L
    OA OA / the length of the segment OA
    1 |5 g; x" a2 v4 C+ |7 O/ FAT A transpose / the transpose of A) m# j( G" U" L" ^" @, N
    A&iexcl;1 A inverse / the inverse of A! u6 _& |0 ^8 I. Y& e+ V, I; m
    2
    9 @7 c! J3 S) I0 h5. Functions
    ( t; {4 C& W. [# |4 e9 j9 Lf(x) fx / f of x / the function f of x( T. L& l. C4 G7 q' h/ s2 V& v
    f : S ! T a function f from S to T# j" d) E2 r/ n7 M: o& a7 n) ^
    x 7! y x maps to y / x is sent (or mapped) to y; @0 d  Q' S: T. \/ E. U& }
    f0(x) f prime x / f dash x / the (&macr;rst) derivative of f with respect to x
    2 k. a3 ?& H+ N9 hf00(x) f double{prime x / f double{dash x / the second derivative of f with
    % _  P7 W0 N: K% l+ y' brespect to x
    9 T3 B, V( }  C% {' B- u0 V0 G0 of000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect
      z+ J- E$ E7 _+ {to x
    - T  U* G( S0 t; z+ r0 m5 }" E; Ef(4)(x) f four x / the fourth derivative of f with respect to x
    ' f! ~1 y/ P/ `& X) V5 w@f
    8 z1 X) }* D6 g& E( C@x1
    + I+ G' c# T, z6 K  i+ l+ n5 u7 Y. d) Fthe partial (derivative) of f with respect to x1  y6 C' k8 p, p: D5 L) C5 J; c
    @2f
    # Y7 _4 m' v1 Q. m: `3 Q$ T6 i: {& B@x21  o! Z% D4 u7 b5 Y) b3 s  U
    the second partial (derivative) of f with respect to x1
    6 A/ u' M( I0 F, iZ# P5 \% B4 V' s2 d; [* f
    1
    - R% H" M3 }: ~# ?8 I0
    7 V; e+ Q8 Q, \$ f. Hthe integral from zero to in&macr;nity
    7 T2 R( w2 s* G9 ^, Ilim+ v" U# V$ ?" F; D! M% v
    x!0
    $ d" y+ l# U. d% U0 Othe limit as x approaches zero( W$ d7 d" O/ q, I; w
    lim* H! ]3 [3 u# I% C3 X+ A% N
    x!+0
    ; [5 W( M- n+ q3 u3 athe limit as x approaches zero from above9 z# E4 Z1 [$ ~4 Y6 Q. _6 p4 B; z. t
    lim  S, l3 }5 }, G, P6 L% K
    x!&iexcl;0
    ' O# Z7 q5 g* Tthe limit as x approaches zero from below
      G) _+ [) h* v1 p# Yloge y log y to the base e / log to the base e of y / natural log (of) y
    # u1 r: _6 ?# t( pln y log y to the base e / log to the base e of y / natural log (of) y
    * L* q& P$ z. d* _; K/ @. {( J! CIndividual mathematicians often have their own way of pronouncing mathematical expressions  a5 w# G* r; w9 m  C  ~
    and in many cases there is no generally accepted \correct" pronunciation.
    7 }! C0 M% ^) V  L. y; NDistinctions made in writing are often not made explicit in speech; thus the sounds fx may2 H& b1 ^3 i: G0 r
    be interpreted as any of: fx, f(x), fx, FX, FX, F&iexcl;&iexcl;X!. The di&reg;erence is usually made clear
    ) z- b1 ^" q% M# Q4 bby the context; it is only when confusion may occur, or where he/she wishes to emphasise2 n+ W1 ]3 J6 E' j8 T" E
    the point, that the mathematician will use the longer forms: f multiplied by x, the function9 l1 U! q3 E2 S6 b& D% ~
    f of x, f subscript x, line FX, the length of the segment FX, vector FX.
    + S* c3 I0 s9 f( h# BSimilarly, a mathematician is unlikely to make any distinction in speech (except sometimes
    # X: {6 h* h9 pa di&reg;erence in intonation or length of pauses) between pairs such as the following:
    : J. Y3 [7 |8 C8 n0 H- Hx + (y + z) and (x + y) + z1 B; W9 u% R4 Z' c. x& o2 U6 W
    pax + b and pax + b
    # C! j7 `$ n" x6 R0 ?an &iexcl; 1 and an&iexcl;1, G& ?6 Y7 D& o" ^3 t0 @
    The primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science5 u5 U+ V" Q; e9 P% _- W( p
    and Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have
    & Y1 j7 Q, Y9 K3 dgiven good comments and supplements.
    $ d$ a# O: j' }3

    常用数学公式(符号)读法.pdf

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