17.2.1999/H,V?aliaho
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
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
x2A x belongs to A / x is an element (or a member) of A
x =2A x does not belong to A / x is not an element (or a member) of A
A‰B A is contained in B / A is a subset of B
A 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
AnB A minus B / the difierence between A and B
A￡B A cross B / the cartesian product of A and B
3,Real numbers
x+ 1 x plus one
x?1 x minus one
x§1 x plus or minus one
xy xy / x multiplied by y
(x?y)(x+y) x minus y,x plus y
x
y x over y
= the equals sign
x = 5 x equals 5 / x is equal to 5
x6= 5 x (is) not equal to 5
1
x·y x is equivalent to (or identical with) y
x6·y x is not equivalent to (or identical with) y
x>y x is greater than y
x?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
jxj mod x / modulus x
x2 x squared / x (raised) to the power 2
x3 x cubed
x4 x to the fourth / x to the power four
xn x to the nth / x to the power n
x?n x to the (power) minus n
px (square) root x / the square root of x
3px cube root (of) x
4px fourth root (of) x
npx nth root (of) x
(x+y)2 x plus y all squared
x
y
·2
x over y all squared
n! n factorial
^x x hat
x x bar
~x x tilde
xi xi / x subscript i / x su–x i / x sub i
nX
i=1
ai the sum from i equals one to nai / the sum as i runs from 1 to n of the ai
4,Linear algebra
kxk the norm (or modulus) of x
!OA OA / vector OA
OA OA / the length of the segment OA
AT A transpose / the transpose of A
A?1 A inverse / the inverse of A
2
5,Functions
f(x) fx / f of x / the function f of x
f,S!T a function f from S to T
x7!y x maps to y / x is sent (or mapped) to y
f0(x) f prime x / f dash x / the (flrst) derivative of f with respect to x
f00(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
f(4)(x) f four x / the fourth derivative of f with respect to x
@f
@x1 the partial (derivative) of f with respect to x1
@2f
@x21 the second partial (derivative) of f with respect to x1
Z 1
0
the integral from zero to inflnity
limx!0 the limit as x approaches zero
limx!+0 the limit as x approaches zero from above
limx!?0 the limit as x approaches zero from below
logey log y to the base e / log to the base e of y / natural log (of) y
lny 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 expres-
sions 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),fx,FX,FX,!FX,The difierence 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
a difierence in intonation or length of pauses) between pairs such as the following:
x+ (y +z) and (x+y) +z
pax+b and pax+b
an?1 and an?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
given good comments and supplements.
3
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
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
x2A x belongs to A / x is an element (or a member) of A
x =2A x does not belong to A / x is not an element (or a member) of A
A‰B A is contained in B / A is a subset of B
A 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
AnB A minus B / the difierence between A and B
A￡B A cross B / the cartesian product of A and B
3,Real numbers
x+ 1 x plus one
x?1 x minus one
x§1 x plus or minus one
xy xy / x multiplied by y
(x?y)(x+y) x minus y,x plus y
x
y x over y
= the equals sign
x = 5 x equals 5 / x is equal to 5
x6= 5 x (is) not equal to 5
1
x·y x is equivalent to (or identical with) y
x6·y x is not equivalent to (or identical with) y
x>y x is greater than y
x?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
jxj mod x / modulus x
x2 x squared / x (raised) to the power 2
x3 x cubed
x4 x to the fourth / x to the power four
xn x to the nth / x to the power n
x?n x to the (power) minus n
px (square) root x / the square root of x
3px cube root (of) x
4px fourth root (of) x
npx nth root (of) x
(x+y)2 x plus y all squared
x
y
·2
x over y all squared
n! n factorial
^x x hat
x x bar
~x x tilde
xi xi / x subscript i / x su–x i / x sub i
nX
i=1
ai the sum from i equals one to nai / the sum as i runs from 1 to n of the ai
4,Linear algebra
kxk the norm (or modulus) of x
!OA OA / vector OA
OA OA / the length of the segment OA
AT A transpose / the transpose of A
A?1 A inverse / the inverse of A
2
5,Functions
f(x) fx / f of x / the function f of x
f,S!T a function f from S to T
x7!y x maps to y / x is sent (or mapped) to y
f0(x) f prime x / f dash x / the (flrst) derivative of f with respect to x
f00(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
f(4)(x) f four x / the fourth derivative of f with respect to x
@f
@x1 the partial (derivative) of f with respect to x1
@2f
@x21 the second partial (derivative) of f with respect to x1
Z 1
0
the integral from zero to inflnity
limx!0 the limit as x approaches zero
limx!+0 the limit as x approaches zero from above
limx!?0 the limit as x approaches zero from below
logey log y to the base e / log to the base e of y / natural log (of) y
lny 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 expres-
sions 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),fx,FX,FX,!FX,The difierence 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
a difierence in intonation or length of pauses) between pairs such as the following:
x+ (y +z) and (x+y) +z
pax+b and pax+b
an?1 and an?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
given good comments and supplements.
3
