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
' @1 Z/ e+ a/ E- g  w0 d9 u9 Gbelow. In general, the shortest versions are preferred (unless greater precision is necessary).
1. Logic
/ u* y% p1 ]( H* ~: C0 l, |9 }9 there exists
$ Z& m* B% q9 ?7 `$ {+ j' H8 for all
p ) q p implies q / if p, then q
, ?+ k: k6 h  t. R2 ]) o7 Vp , q p if and only if q /p is equivalent to q / p and q are equivalent
: V; }: l0 C) J9 z  H2. Sets
x 2 A x belongs to A / x is an element (or a member) of A
1 h9 Y& h) }. Z7 a+ \" |9 C7 Nx =2 A x does not belong to A / x is not an element (or a member) of A
A ½ B A is contained in B / A is a subset of B
3 @) I9 N- k: I% b8 c6 AA 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
A n B A minus B / the di®erence between A and B
( |- q- C) s8 q% O: DA £ B A cross B / the cartesian product of A and B
3. Real numbers
) W1 J% ^3 Q; Gx + 1 x plus one
x ¡ 1 x minus one
x § 1 x plus or minus one
8 p! k8 d5 o% D( \3 `xy xy / x multiplied by y
; {3 i1 M! Z+ Z(x ¡ y)(x + y) x minus y, x plus y
x
# R$ G3 d# Q) Y! W3 }/ I1 Ay
3 s* F9 }+ m7 X- n' R8 G/ Mx over y
- ^! \" a( o' _2 C= the equals sign
, \  F8 G& D0 X% e/ i7 o7 v9 Lx = 5 x equals 5 / x is equal to 5
, W( ?! h3 `+ Dx 6= 5 x (is) not equal to 5
8 j: K7 Y- V4 M. E+ w1
& G* v" ]" {% k7 m8 L* |x ´ y x is equivalent to (or identical with) y
x 6´ y x is not equivalent to (or identical with) y
# f9 k& v: _6 M. F* Vx > y x is greater than y
4 o6 l1 ^$ K, W# Ox ¸ y x is greater than or equal to y
x < y x is less than y
x · y x is less than or equal to y
0 < x < 1 zero is less than x is less than 1
0 · x · 1 zero is less than or equal to x is less than or equal to 1
3 r* B, w8 @0 k. {9 @3 L; g4 y& mjxj mod x / modulus x
% K. y# ^+ ~3 kx2 x squared / x (raised) to the power 2
x3 x cubed
# m. @1 J2 [( e( O! W3 Jx4 x to the fourth / x to the power four
6 e. g7 B% p4 n$ Z7 ?9 Cxn 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 F% x( {/ Y2 s" ip3 x cube root (of) x
, c3 t* {3 w/ v4 C1 w3 Q  sp4 x fourth root (of) x
npx nth root (of) x
(x + y)2 x plus y all squared
&sup3;x
( I; }8 e$ b5 I! r  hy
/ g' v' O; C- \8 r/ K( q&acute;2
x over y all squared
n! n factorial
^x x hat
&sup1;x x bar
~x x tilde
xi xi / x subscript i / x su±x i / x sub i
4 |4 L1 S# G; l1 ?$ I0 L# S1 pXn
i=1
5 f7 g4 ~" a; _8 s. o4 Nai the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai
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
AT A transpose / the transpose of A
# c8 ?( w5 m' Q7 {- F, XA&iexcl;1 A inverse / the inverse of A
( M; v' h! ?1 h$ E  |1 Z+ R* L3 p2
7 L$ X( ]+ S% W- f4 ?+ y5. Functions
f(x) fx / f of x / the function f of x
f : S ! T a function f from S to T
x 7! y x maps to y / x is sent (or mapped) to y
f0(x) f prime x / f dash x / the (&macr;rst) derivative of f with respect to x
, q: r$ I, o: X- X# a& }$ zf00(x) f double{prime x / f double{dash x / the second derivative of f with
respect to x
f000(x) f triple{prime x / f triple{dash x / the third derivative of f with respect
to x
$ w4 Q' ?4 \2 mf(4)(x) f four x / the fourth derivative of f with respect to x
@f
- r  @$ y8 U* b0 Y8 e: b@x1
the partial (derivative) of f with respect to x1
@2f
@x21
the second partial (derivative) of f with respect to x1
Z
1
' R  t& ~% l0 w2 d; H) l0
the integral from zero to in&macr;nity
lim
x!0
7 }9 q' x% m6 o- [2 Jthe limit as x approaches zero
; E- s1 @* n; slim
$ c8 O& p% |6 S" L5 U" zx!+0
the limit as x approaches zero from above
) R4 h: z5 A+ Z; qlim
x!&iexcl;0
the limit as x approaches zero from below
. N9 `  |! p3 j: z6 f' [) hloge y log y to the base e / log to the base e of y / natural log (of) y
( }5 ]- F$ Z. r% `+ c0 \+ T0 a: vln y log y to the base e / log to the base e of y / natural log (of) y
" X% @, ~. z3 i- O' v2 Q9 FIndividual mathematicians often have their own way of pronouncing mathematical expressions
) D2 n$ ~4 b4 ~! [9 o- i* }2 \, a( W8 ^and in many cases there is no generally accepted \correct" pronunciation.
" `% q7 Y' y: U/ |8 y) l! yDistinctions made in writing are often not made explicit in speech; thus the sounds fx may
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
the 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.
Similarly, a mathematician is unlikely to make any distinction in speech (except sometimes
7 G- x' y0 V0 Z$ U0 e" \$ Ya di&reg;erence in intonation or length of pauses) between pairs such as the following:
x + (y + z) and (x + y) + z
pax + b and pax + b
7 y2 K; ^+ y* v% T) @; P6 [2 [an &iexcl; 1 and an&iexcl;1
The primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science
and Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have
! t6 o5 r) @1 O2 l0 qgiven good comments and supplements.
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