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 集合
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 cro B / the cartesian product of A and B 3.Real numbers x+1 x-1 x±1 xy x plus one x minus one x plus or minus one xy / x multiplied by y
x minus y, x plus y (x-y)(x+y) = x=5 x≠5 the equals sign
x equals 5 / x is equal to 5 x (is) not equal to 5
x≡y x is equivalent to (or identical with) y x>y x≥y x
x is greater than or equal to y x is le than y x≤y x is le than or equal to y
zero is le than x is le than 1
zero is le than or equal to x is le than or equal to 1 0
x squared / x (raised) to the power 2 x cubed
x to the fourth / x to the power 4 x to the nth / x to the power n x to the (power) minus n
(square) root x / the square root of x
cube root (of) x fourth root (of) x nth root (of) x x的三次根 x的四次根 x的n次根
(x+y)2 x plus y all squared n! x^ x¯ x˜ xi n factorial x hat x bar x tilde
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 这里应该是写在字母上的一短杠
OA¯ OA / the length of the segment OA 同上，长杠 AT A−1 A transpose / the transpose of A 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 4应该是上角标
∂f/∂x1 the partial (derivative) of f with respect to x1 ∂2f/∂x12 ∫0∞ the second partial (derivative) of f with respect to x1
the integral from zero to infinity
limx→0 the 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
