# 数学公式的英文表达

## # Logic

$∃$ there exist

$∀$ 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 diference 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

$=$ the equals sign

$x=5$ x equals 5 / x is equal to 5

$x≠5$ x (is) not equal to 5

$x≡y$ x is equivalent to (or identical with) y

$x>y$ x is greater than y

$x≥y$ x is greater than or equal to y

$x x is less than y

$x≤y$ x is less than or equal to y

$0 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 4

$x^n$ x to the nth / x to the power n

$x^(−n)$ x to the (power) minus n

$\sqrt{x}$ root x / the square root of x

$\sqrt[3]{x}$ cube root (of) x

$\sqrt[4]{x}$ fourth root (of) x

$\sqrt[n]{x}$ n-th root (of) x

$(x+y)^2$ x plus y all squared

$n!$ n factorial

$\hat{x}$ x hat

$\bar{x}$ x bar

$\tilde{x}$ x tilde

$x_i$ xi / x subscript i / x suffix i / x sub i

$\sum_{i=1}^{n}a_i$ the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai

## # Linear algebra

$\left \| x \right \|$ the norm (or modulus) of x

$\overrightarrow{OA}$ OA / vector OA

$\bar{OA}$ OA / the length of the segment OA

$A^T$ A transpose / the transpose of A

$A^{-1}$ A inverse / the inverse of A

## # Functions

$f(x)$ fx / f of x / the function f of x

$f:S→T$ a function f from S to T

$x→y$ x maps to y / x is sent (or mapped) to y

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

$f''(x)$ f double-prime x / f double-dash x / the second derivative of f with respect to x

$f'''(x)$ triple-prime x / f triple-dash x / the third derivative of f with respect to x

$f_{x}^{4}$ f four x / the fourth derivative of f with respect to x

$\frac{\partial f}{\partial x_1}$ the partial (derivative) of f with respect to $x_1$

$\frac{\partial^2 f}{\partial x_{1}^2}$ the second partial (derivative) of f with respect to $x_1$

$\int_{0}^{\infty }$ the integral from zero to infinity

$\lim_{x \rightarrow 0}$ the limit as x approaches zero

$\lim_{x \rightarrow 0^+}$ the limit as x approaches zero from above

$\lim_{x \rightarrow 0^-}$ 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

$\ln y$ log y to the base e / log to the base e of y / natural log (of) y

Last update: September 17, 2021 14:48