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.
