1.Logic

∃there exist

∀for all（看到有人说是for any）

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 diference 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

= 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<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

x2x squared / x (raised) to the power 2

x3x cubed

x4 x to the fourth / x to the power 4

xn x to the nth / x to the power n

x(−n)x to the (power) minus n

x的平方根(square) root x / the square root of x

x的三次根cube root (of) x

x的四次根fourth root (of) x

x的n次根nth root (of) x

(x+y)2 x plus y all squared

n! n factorial

x^x hat

x¯ x bar

x˜ x tilde

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

∑(i=1~n) 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

‖x‖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−1 A inverse / the inverse of A

5. 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 (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/∂x12 the second partial (derivative) of f with respect to x1

∫0∞ the integral from zero to infinity

limx→0the limit as x approaches zero

limx→0+the limit as x approaches zero from above

limx→0−the limit as x approaches zero from below

logey 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