O(1) 的小樂

常用的數學英語表述

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 ˉ           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 ˉ           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
一般詞匯
    數學 mathematics, maths(BrE), math(AmE)
    公理 axiom
    定理 theorem
    計算 calculation
    運算 operation
    證明 prove
    假設 hypothesis, hypotheses(pl.)
    命題 proposition
    算術 arithmetic
    加 plus(prep.), add(v.), addition(n.)
    被加數 augend, summand
    加數 addend
    和 sum
    減 minus(prep.), subtract(v.), subtraction(n.)
    被減數 minuend
    減數 subtrahend
    差 remainder
    乘
times(prep.), multiply(v.), multiplication(n.)
    被乘數 multiplicand, faciend
    乘數 multiplicator
    積 product
    除 divided by(prep.), divide(v.), division(n.)
    被除數 dividend
    除數 divisor
    商 quotient
    等于 equals, is equal to, is equivalent to
    大于 is greater than
    小于 is lesser than
    大于等于 is equal or greater than
    小于等于 is equal or lesser than
    運算符 operator
    數字 digit
    數 number
    自然數 natural number
    整數 integer
    小數 decimal
    小數點 decimal point
    分數 fraction
    分子 numerator
    分母 denominator
    比 ratio
    正 positive
    負 negative
    零 null, zero, nought, nil
    十進制 decimal system
    二進制 binary system
    十六進制 hexadecimal system
    權 weight, significance
    進位 carry
    截尾 truncation
    四舍五入 round
    下舍入 round down
    上舍入 round up
    有效數字 significant digit
    無效數字 insignificant digit
    代數 algebra
    公式 formula, formulae(pl.)
    單項式 monomial
    多項式 polynomial, multinomial
    系數 coefficient
    未知數 unknown, x-factor, y-factor, z-factor
    等式，方程式 equation
    一次方程 simple equation
    二次方程 quadratic equation
    三次方程 cubic equation
    四次方程 quartic equation
    不等式 inequation
    階乘 factorial
    對數 logarithm
    指數，冪 exponent
    乘方 power
    二次方，平方 square
    三次方，立方 cube
    四次方 the power of four, the fourth power
    n次方 the power of n, the nth power
    開方 evolution, extraction
    二次方根，平方根 square root
    三次方根，立方根 cube root
    四次方根 the root of four, the fourth root
    n次方根 the root of n, the nth root
    集合 aggregate
    元素 element
    空集 void
    子集 subset
    交集 intersection
    并集 union
    補集 complement
    映射 mapping
    函數 function
    定義域 domain, field of definition
    值域 range
    常量 constant
    變量 variable
    單調性 monotonicity
    奇偶性 parity
    周期性 periodicity
    圖象 image
    數列，級數 series
    微積分 calculus
    微分 differential
    導數 derivative
    極限 limit
    無窮大 infinite(a.) infinity(n.)
    無窮小 infinitesimal
    積分 integral
    定積分 definite integral
    不定積分 indefinite integral
    有理數 rational number
    無理數 irrational number
    實數 real number
    虛數 imaginary number
    復數 complex number
    矩陣 matrix
    行列式 determinant
    幾何 geometry
    點 point
    線 line
    面 plane
    體 solid
    線段 segment
    射線 radial
    平行 parallel
    相交 intersect
    角 angle
    角度 degree
    弧度 radian
    銳角 acute angle
    直角 right angle
    鈍角 obtuse angle
    平角 straight angle
    周角 perigon
    底 base
    邊 side
    高 height
    三角形 triangle
    銳角三角形 acute triangle
    直角三角形 right triangle
    直角邊 leg
    斜邊 hypotenuse
    勾股定理 Pythagorean theorem
    鈍角三角形 obtuse triangle
    不等邊三角形 scalene triangle
    等腰三角形 isosceles triangle
    等邊三角形 equilateral triangle
    四邊形 quadrilateral
    平行四邊形 parallelogram
    矩形 rectangle
    長 length
    寬 width