2024年3月16日 · 首先是证明0.999…=1的方法： 设0.999…=x 10x = 9.999… 10x -x = 9 9x = 9 x = 1那么既然 0.999…… 显示全部

In mathematics, 0.999... (also written as 0.9, 0.. 9, or 0. (9)) is a repeating decimal that is an alternative way of writing the number 1. Following the standard rules for representing numbers in decimal notation, its value is the smallest number greater than or equal to every number in the sequence 0.9, 0.99, 0.999, ....

2023年9月1日 · 威廉·拜尔斯（William Byers）在《How Mathematicians Think》中评价这个证明：“0.999...... 既可以代表把无限个分数加起来的过程，也可以代表这个过程的结果。 许多学生仅仅把 0.999...... 看作一个过程，但是 1 是一个数，过程怎么会等于一个数呢？ 这就是数学中的二义性⋯⋯他们并没有发现其实这个无限的过程可以理解成一个数。

2024年10月15日 · 视觉的误导 ：0.999… 和 1 看起来是两个不同的数，人们习惯于根据视觉差异来判断它们。直觉告诉我们，0.999… 应该比 1 「小那么一点点」。 对无限的误解 ：很多人认为 0.999… 总是「无限接近」1，但不会等于 1。其实，这是对「无限」的误解。

2018年5月12日 · Several years ago, while traveling with co-workers, the subject of .99999… ( that’s .9 with a bar over it, or .9 repeating infinitely ) being equal to 1 came up. While the assertion initially...

Consider the real number that is represented by a zero and a decimal point, followed by a never-ending string of nines: 0.99999… It may come as a surprise when you first learn the fact that this real number is actually EQUAL to the integer 1. A common argument that is often given to show this is as follows.

2011年5月6日 · What is it short hand for? It literally means the act of appending 9’s after the decimal point infinitely. Mathematically that means 0.9 + 0.09 + 0.009 + …, which we write in shorthand (imagine the correct mathematical notation): SUM_(from x=0 to infinity) of (0.9 * 10^x) But how do you calculate an infinite sum? That by definition is

So the common proof that I have seen that 0.999... (that is 9 repeating to infinity in the decimal) is equal to 1 is: let x = 0.999... 10x = 9.999... 10x - x = 9.999... - 0.999... 9x = 9. x = 1.

S = 0.9+0.09+0.009+… = \frac{0.9(1-0.1^\omega)}{1-0.1}=1-0.1^\omega. 而级数的极限是指“级数和”的实数部分，即： L=st(S)= st(1-0.1^\omega) =1 . 其中的st是标准化函数，可用于舍弃无穷小量，和极限符号lim的作用相似，详见第一章。

喜欢数学的朋友会发现，在人们的视野中经常出现许多数学问题，例如：“0.5×0.8=0.4”、“0.999...=1”。他们有时会在抖音的评论区掀起惊涛骇浪，有时也会在知乎等平台掀起一波又一波的风雨。 而今天，我打算深入…