“区间”概念是高中数学的基础概念,但在笔者第二轮执教高一的过程中对此产生了诸多疑惑.通过对学生常见错误及惯用写法的深入探究,豁然开朗,现整理成文,敬请指正.一、背景:单调区间能否用“∪”连接众所周知,函数f(x)=1/x的单调递减区间是(-∞,0),(0,+∞),而不是(-∞,0)∪(0,+∞).对这一问题的解释,通常是举如下的反例:-1∈(-∞,0)∪(0,+∞),1∈ “Interval ” concept is the basic concept of high school mathematics, but in the process of the second round of the teaching of the author has a lot of doubts about this .Through the common mistakes and idioms of students to explore in depth, is now clear, , Please correct me First, the background: Monotone interval can use “∪ ” connection As we all know, monotonically decreasing range of the function f (x) = 1 / x is (-∞, 0), (0, + ∞) Instead of (-∞, 0) ∪ (0, + ∞). An explanation of this problem is usually the following counterexample: -1∈ (-∞, 0) ∪ (0, + ∞), 1∈