## How to read / present math, equation, formula in English?

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**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

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**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 difference between A and B

A×B A cross B / the Cartesian product of A and B

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**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

x

^{2 }x squared / x (raised) to the power 2
x

^{3 }x cubed
x

^{4}x to the fourth / x to the power 4
x

^{n}x to the nth / x to the power n
x

^{ (−n) }x to the (power) minus n
x^2 (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
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}
‖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
lny log y to the base e / log to the base e of y / natural log (of) y

how can i read math set in English?

how to read math formulas in English?
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