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Pronunciation of Mathematical Expressions The pronunciations of the most common mathematical expressions are given in the list below. In general, the shortest versions are preferred (unless greater precision is necessary). 1��Logic

?
?

there Exists for All / Any p implies q / if p, then q p if and only if (iff) q / p is equivalent to q / p and q are equivalent

p?q
p?q

2��Sets
x? A
x? A
A? B A? B

x belongs to A / x is an element (or a member) of A x does not belong to A / x is not an element (or a member) of A A is contained in B / A is a subset of B A contains B / B is a subset of A A cap B / A meet B / A intersection B A cup B / A join B / A union B A minus B / the difference between A and B A cross B / the Cartesian product of A and B

A? B A? B

A\ B
A? B

3��Real numbers
x ?1
x ?1 x ?1
xy

x plus one x minus one x plus or minus one xy / x multiplied by y x minus y, x plus y

( x ? y)(x ? y)

x y

x over y / x on y the equals sign x equals 5 / x is equal to 5 x (is) not equal to 5 x is equivalent to (or identical with) y x is not equivalent to (or identical with) y x is greater than y x is greater than or equal to y x is less than y x is less than or equal to y zero is less than x is less than 1 zero is less than or equal to x is less than or equal to 1 mod x / modulus x / absolute value of x x squared / x (raised) to the power 2 x cubed x to the fourth / x to the power four x to the nth / x to the power n x to the (power) minus n (square) root x / the square root of x cube root (of) x fourth root (of) x nth root (of) x x plus y all squared x over y all squared n factorial

��
x?5 x?5
x? y

x? y
x? y

x? y
x? y

x? y

0 ? x ?1 0 ? x ?1

x
x2 x3

x4 xn
x ?n

x
3

x x x

4

n

( x ? y) 2
? ? ? ? x? ? y? ?
2

n!

? x
x

x hat x bar x tilde xi / x subscript i / x suffix i / x sub i xi / x superscript i / x superfix i / x super i
i

~ x

xi
xi

?a
i ?1

n

the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai

4��Linear algebra

x

the norm (or modulus) of x OA / vector OA OA / the length of the segment OA A transpose / the transpose of A A inverse / the inverse of A

OA
OA
AT A ?1

5��Functions
f (x) f : S ?T

f x / f of x / the function f of x a function f from S to T x maps to y / x is sent (or mapped) to y f prime x / f dash x / the (first) derivative of f with respect to x f double�Cprime x / f double�Cdash x / the second derivative of f with respect to x

x? y
f ?(x)

f ??(x) f ???(x)

f triple�Cprime x / f triple�Cdash x / the third derivative of f with respect to x f four x / the fourth derivative of f with respect to x partial F on partial x / partial differential F on x

f ( 4) ( x)
?F ?x

?f ?x1

the partial (derivative) of f with respect to x1

?2 f 2 ?x1

the second partial (derivative) of f with respect to x1

?

?

0

the integral from zero to infinity the limit as x approaches zero the limit as x approaches zero from above the limit as x approaches zero from below log y to the base e/ log to the base e of y / natural log (of) y log y to the base e / log to the base e of y / natural log (of) y

lim
x?0

x ? ?0

lim lim

x ? ?0

loge y
ln y

Individual mathematicians often have their own way of pronouncing mathematical expressions and in many cases there is no generally accepted ��correct�� pronunciation. Distinctions made in writing are often not made explicit in speech; thus the sounds fx may be interpreted as any of: fx,

f ( x), f x , FX , FX , FX . The difference is usually

made clear by the context; it is only when confusion may occur, or where he/she wishes to emphasize 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 a difference in intonation or length of pauses) between pairs such as the following:
x ? ( y ? z ) and ( x ? y ) ? z

ax ? b
a n ?1

and and

ax? b
a n?1

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52

four fifths / 4 on 5 zero point zero two five thirty-eight point four nine two per cent the second power of five / five to the power two the square root of x six times the seventh power of ten plus ; positive minus ; negative multiplied by ; times divided by is equal to ; equals round brackets ; parentheses (parenthesis) imaginary unit factorial a sine of x arc sine of x the product of the terms indicated the sum of the terms indicated b prime b second prime

x
6 ? 107

?
?

?; /

= () i; j
a!
sin x arcsin x
?

��
b? b ??

b2
bm ?

b sub two b second prime sub m the first derivative of y with respect to x the second derivative of y with respect to x integral between limits a and b x approaches to infinity a plus b is equal to c a minus b equals c s equals v multiplied by t v equals s divided by t a plus b minus c multiplied by d, all divided by e equals f C over R equals G divided by the sum of one and H times G

dy / dx

d 2 y / dx2

?

b

a

x ??
a?b ? c
a?b ? c

s ? vt
v ? s/t
(a ? b ? c ? d ) / e ? f C / R ? G /(1 ? GH )