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