| 1.Logic
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| ∃
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| there exist |
| ∀
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| for all |
| p⇒q
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| p implies q / if p, then q |
| p⇔q
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| p if and only if q /p is equivalent to q / p and q are equivalent |
| 2.Sets
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| x∈A
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| x belongs to A / x is an element (or a member) of A |
| x∉A
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| x does not belong to A / x is not an element (or a member) of A |
| A⊂B
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| A is contained in B / A is a subset of B |
| A⊃B
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| A contains B / B is a subset of A |
| A∩B
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| A cap B / A meet B / A intersection B |
| A∪B
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| A cup B / A join B / A union B |
| A\B
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| A minus B / the diference between A and B |
| A×B
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| A cross B / the cartesian product of A and B |
| 3. Real numbers
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| |
| x+1
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| x plus one |
| x-1
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| x minus one |
| x±1
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| x plus or minus one |
| xy
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| xy / x multiplied by y |
|
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| (x - y)(x + y)
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| x minus y, x plus y |
|
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| x y
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| x over y |
| =
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| the equals sign |
| x = 5
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| x equals 5 / x is equal to 5 |
| x≠5
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| x (is) not equal to 5 |
| x≡y
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| x is equivalent to (or identical with) y |
| x ≡ y
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| x is not equivalent to (or identical with) y |
| x > y
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| x is greater than y |
| x≥y
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| x is greater than or equal to y |
| x < y
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| x is less than y |
| x≤y
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| x is less than or equal to y |
| 0 < x < 1
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| zero is less than x is less than 1 |
| 0≤x≤1
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| zero is less than or equal to x is less than or equal to 1 |
| | x |
|
| mod x / modulus x |
| x 2
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| x squared / x (raised) to the power 2 |
| x 3
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| x cubed |
| x 4
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| x to the fourth / x to the power four |
| x n
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| x to the nth / x to the power n |
| x −n
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| x to the (power) minus n |
| x
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| (square) root x / the square root of x |
| x 3
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| cube root (of) x |
| x 4
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| fourth root (of) x |
| x n
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| nth root (of) x |
| ( x+y ) 2
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| x plus y all squared |
| ( x y ) 2
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| x over y all squared |
| n!
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| n factorial |
| x ^
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| x hat |
| x ¯
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| x bar |
| x ˜
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| x tilde |
| x i
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| xi / x subscript i / x suffix i / x sub i |
| ∑ i=1 n a i
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| 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
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| |
| ‖ x ‖
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| the norm (or modulus) of x |
| OA →
|
| OA / vector OA |
| OA ¯
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| OA / the length of the segment OA |
| A T
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| A transpose / the transpose of A |
| A −1
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| A inverse / the inverse of A |
| 5. Functions
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| |
| f( x )
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| fx / f of x / the function f of x |
| f:S→T
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| a function f from S to T |
| x→y
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| x maps to y / x is sent (or mapped) to y |
| f'( x )
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| f prime x / f dash x / the (first) derivative of f with respect to x |
| f''( x )
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| f double-prime x / f double-dash x / the second derivative of f with respect to x |
| f'''( x )
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| triple-prime x / f triple-dash x / the third derivative of f with respect to x |
| f (4) ( x )
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| f four x / the fourth derivative of f with respect to x |
| ∂f ∂ x 1
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| the partial (derivative) of f with respect to x1 |
| ∂ 2 f ∂ x 1 2
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| the second partial (derivative) of f with respect to x1 |
| ∫ 0 ∞
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| the integral from zero to infinity |
| lim x→0
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| the limit as x approaches zero |
| lim x→ 0 +
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| the limit as x approaches zero from above |
| lim x→ 0 −
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| the limit as x approaches zero from below |
| log e y
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| log y to the base e / log to the base e of y / natural log (of) y |
| lny
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| log y to the base e / log to the base e of y / natural log (of) y |
