Some Mathematics Formulas 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 ¯ 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 ¯ 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