Math Functions
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
= 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 x2 x squared / x (raised) to the power 2 x3 x 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
∃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
= 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 x2 x squared / x (raised) to the power 2 x3 x 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