数学公式的英语读法/Saying Math Functions in English

1.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  
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  
x y       x over 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 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  
x 3       cube root (of) x  
x 4       fourth root (of) x  
x n       nth root (of) x  
( x+y ) 2       x plus y all squared  
( x y ) 2       x over y all squared  
n!       n factorial  
x ^       x hat  
x ˉ       x bar  
x ˜       x tilde  
x i       xi / x subscript i / x suffix i / x sub i  
∑ i=1 n 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    
‖ x ‖       the norm (or modulus) of x  
OA →       OA / vector OA  
OA ˉ       OA / the length of the segment OA  
A T       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 ∂ x 1       the partial (derivative) of f with respect to x1  
∂ 2 f ∂ x 1 2       the second partial (derivative) of f with respect to x1  
∫ 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  
ln(y)       log y to the base e / log to the base e of y / natural log (of) y