﻿Pronunciation of Mathematical expressions | 数学补习,家教,辅导,补课 Sydney Mathematics Coaching,Math Tutor

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
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 ∈ 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
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
|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
4. 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
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
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.