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).

- Logic

∃ there exists

∀ 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 - Sets

x ∈ A x belongs to A / x is an element (or a member) of A

x / ∈ 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 \ B A minus B / the difference between A and B

A × B A cross B / the cartesian product of A and B - 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

|x| mod x / modulus x

x 2 x squared / x (raised) to the power 2

x 3 x cubed

x 4 x to the fourth / x to the power four

x n x to the nth / x to the power n

x −n x to the (power) minus n

√ x

(square) root x / the square root of x

3

√ x

cube root (of) x

4

√ x

fourth root (of) x

n

√ x

nth root (of) x

(x + y) 2 x plus y all squared

‡ x

y

· 2

x over y all squared

n! n factorial

ˆ x x hat

¯ x x bar

˜ x x tilde

x i xi / x subscript i / x suffix i / x sub i

n

X

i=1

a i the sum from i equals one to n a i / the sum as i runs from 1 to n of the a i - Linear algebra

kxk the norm (or modulus) of x

−−→

OA OA / vector OA

OA OA / the length of the segment OA

A T A transpose / the transpose of A

A −1 A inverse / the inverse of A

2 - 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

f 0 (x) f prime x / f dash x / the (first) derivative of f with respect to x

f 00 (x) f double–prime x / f double–dash x / the second derivative of f with

respect to x

f 000 (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

∂x 1

the partial (derivative) of f with respect to x 1

∂ 2 f

∂x 2

1

the second partial (derivative) of f with respect to x 1

Z

∞

0

the integral from zero to infinity

lim

x→0

the limit as x approaches zero

lim

x→+0

the limit as x approaches zero from above

lim

x→−0

the limit as x approaches zero from below

log e y 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 expressions and in many cases there is no generally accepted “correct” pronunciation.