常用数学符号的英文表达

常用数学符号的英文表达

第一章函数与极限

Chapter1 Function and Limit

集合set

元素element

子集subset

空集empty set

并集union

交集intersection

差集difference of set

基本集basic set

补集complement set

直积direct product

笛卡儿积Cartesian product

开区间open interval

闭区间closed interval

半开区间half open interval

有限区间finite interval

区间的长度length of an interval

无限区间infinite interval

领域neighborhood

领域的中心centre of a neighborhood

领域的半径radius of a neighborhood

左领域left neighborhood

右领域right neighborhood

映射mapping

X到Y的映射mapping of X ontoY

满射surjection

单射injection

一一映射one-to-one mapping

双射bijection

算子operator

变化transformation

函数function

逆映射inverse mapping

复合映射composite mapping

自变量independent variable

因变量dependent variable

定义域domain

函数值value of function

函数关系function relation

值域range

自然定义域natural domain

单值函数single valued function

多值函数multiple valued function

单值分支one-valued branch

函数图形graph of a function

绝对值函数absolute value

符号函数sigh function

整数部分integral part

阶梯曲线step curve

当且仅当if and only if(iff)

分段函数piecewise function

上界upper bound

下界lower bound

有界boundedness

无界unbounded

函数的单调性monotonicity of a function

单调增加的increasing

单调减少的decreasing

单调函数monotone function

函数的奇偶性parity(odevity) of a function 对称symmetry

偶函数even function

奇函数odd function

函数的周期性periodicity of a function

周期period

反函数inverse function

直接函数direct function

复合函数composite function

中间变量intermediate variable

函数的运算operation of function

基本初等函数basic elementary function

初等函数elementary function

幂函数power function

指数函数exponential function

对数函数logarithmic function

三角函数trigonometric function

反三角函数inverse trigonometric function 常数函数constant function

双曲函数hyperbolic function

双曲正弦hyperbolic sine

双曲余弦hyperbolic cosine

双曲正切hyperbolic tangent

反双曲正弦inverse hyperbolic sine

反双曲余弦inverse hyperbolic cosine

反双曲正切inverse hyperbolic tangent

极限limit

数列 sequence of number

收敛 convergence

收敛于 a converge to a

发散 divergent

极限的唯一性 uniqueness of limits

收敛数列的有界性 boundedness of a convergent sequence

子列 subsequence

函数的极限 limits of functions

函数()f x 当x 趋于x 0时的极限 limit of functions ()f x as x approaches x 0 左极限 left limit

右极限 right limit

单侧极限 one-sided limits

水平渐近线 horizontal asymptote

无穷小 infinitesimal

无穷大 infinity

铅直渐近线 vertical asymptote

夹逼准则 squeeze rule

单调数列 monotonic sequence

高阶无穷小 infinitesimal of higher order

低阶无穷小 infinitesimal of lower order

同阶无穷小 infinitesimal of the same order

等阶无穷小 equivalent infinitesimal

函数的连续性 continuity of a function

增量 increment

函数()f x 在x 0连续 the function ()f x is continuous at x 0

左连续 left continuous

右连续 right continuous

区间上的连续函数 continuous function

函数()f x 在该区间上连续 function ()f x is continuous on an interval