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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
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
x 2 A x belongs to A / x is an element (or a member) of A
x =2 A 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
A n B A minus B / the di?rence 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
x 6= 5 x (is) not equal to 5
1
x ?y x is equivalent to (or identical with) y
x 6?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☆ x to the (power) minus n
px (square) root x / the square root of x
3 px cube root (of) x
4 px fourth root (of) x
npx nth root (of) x
(x + y)2 x plus y all squared

y ?
x over y all squared
n! n factorial
^x x hat

~x x tilde
xi xi / x subscript i / x su兵 i / x sub i
n Xi=1
ai 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
! OA OA / vector OA
OA OA / the length of the segment OA
AT A transpose / the transpose of A
A? 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
x 7! y x maps to y / x is sent (or mapped) to y
f0(x) f prime x / f dash x / the (?st) 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 in?ity
lim
x!0
the limit as x approaches zero
lim
x!+0
the limit as x approaches zero from above
lim
x!?
the limit as x approaches zero from below
loge y log y to the base e / log to the base e of y / natural log (of) y
ln 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.
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 di?rence 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 di?rence 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?

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