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
; O5 ]- m" Y  ?  I/ Fbelow. In general, the shortest versions are preferred (unless greater precision is necessary).
1. Logic
9 there exists
8 for all
p ) q p implies q / if p, then q
p , q p if and only if q /p is equivalent to q / p and q are equivalent
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 A
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
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
3 |8 c9 v3 M/ p: qA £ B A cross B / the cartesian product of A and B
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
xy xy / x multiplied by y
(x ¡ y)(x + y) x minus y, x plus y
x
) ]) Q) a4 f2 d+ H, My
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
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
x < y x is less than y
9 Q# ^. G1 K8 {- C- i# nx · 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
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 2
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
px (square) root x / the square root of x
) z" Y2 M! s3 S; h- v, T) Bp3 x cube root (of) x
p4 x fourth root (of) x
npx nth root (of) x
, d, Z* c2 g: C) p% j9 }( l& D(x + y)2 x plus y all squared
&sup3;x
y
" A, K6 V) n& O0 p) A3 S" i& U&acute;2
x over y all squared
n! n factorial
^x x hat
3 @% A, z  c0 V% C7 j&sup1;x x bar
~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
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 ai
4. Linear algebra
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 A
2
5. Functions
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 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
5 Y# g2 g! C# o8 e$ I4 N! Xf00(x) f double{prime x / f double{dash x / the second derivative of f with
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
to x
f(4)(x) f four x / the fourth derivative of f with respect to x
; b8 o, p% N' o@f
@x1
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! @@x21
the second partial (derivative) of f with respect to x1
) l! S) x3 p# b: e5 zZ
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
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
the limit as x approaches zero from above
* i  ~7 A# R+ d- W+ ^lim
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
Individual mathematicians often have their own way of pronouncing mathematical expressions
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 may
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 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.
5 o4 R/ m, w7 J: _- J6 ^2 L7 eSimilarly, a mathematician is unlikely to make any distinction in speech (except sometimes
a 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
% 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
given good comments and supplements.
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