函数单调性相关英文文献.docxVIP

翻译资料The monotonicity of the function函数的单调性也叫函数的增减性。函数的单调性是对某个区间而言的，它是一个局部概念。定义Definition一般地，设函数f(x）的定义域为I：In general, a function f (x) domain of I:如果对于属于I内某个区间上的任意两个自变量的值x1、x2，当x1x2时都有f(x1)≥f(x2).那么就说f(x）在这个区间上是增函数(另一种说法为单调不减函数)。如果f(x1)f(x2)，那么就说f(x）在这个区间上是严格增函数（另一种说法是增函数）。If for any belongs to some interval I on the two variables x1, X2, when x1x2 is f (x1) ≥ f (x2). Then f (x) in this interval is an increasing function of (another argument is monotone non decreasing function). If f (x1) f (x2), then f (x) in this interval is strictly increasing function (another story is the increasing function).如果对于属于I内某个区间上的任意两个自变量的值x1、x2，当x1x2时都有f(x1)≤f(x2).那么就是f(x）在这个区间上是减函数(另一种说法为单调不增函数)。如果f(x1)f(x2)，那么就说f(x）在这个区间上是严格减函数（另一种说法是减函数）。If for any belongs to some interval I on the two variables x1, X2, when x1x2 is f (x1) ≤ f (x2) f (x). It is in this interval is a decreasing function of (another term for monotone non increasing function). If f (x1) f (x2), then f (x) in this interval is strictly decreasing function (another argument is a decreasing function).为了回避歧义，下文采取单调不减函数，严格增函数，单调不增函数，严格减函数等术语。In order to avoid ambiguity, below the monotone non decreasing functions, strictly increasing function, monotone non increasing function, strictly decreasing function such as terminology.Nature如果函数y=f(x）在某个区间是增函数或减函数。那么就说函数y=f(x）在这一区间具有（严格的）单调性，这一区间叫做y= f(x）的单调区间，在单调区间上增函数的图像是上升的，减函数的图像是下降的。If the function y=f (x) in a certain interval is the increasing function or decreasing function. Then said the function y=f (x) is in the range of (strict) monotonicity, this interval is called y= f (x) monotone interval, image enhancement functions in monotone interval is rising, image reduction function is declining.注意：Be careful.函数的单调性也叫函数的增减性；The monotonicity of the monotonicity of the function is also called function;函数的单调性是对某个区间而言的，它是一个局部概念。The monotonicity of the function on an interval is concerned, it is a local concept.Extension在数学中在有序集合之间的函数是单调(monotone)的，如果它们保持给定的次序。这些函数最先出现在微积分中后来推广到序理论中