知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。

@turkeyhundt I don't like appealing to "common sense" results like this because it would lead one to believe that negative binomials (for example) aren't a thing due to the factorial function, and yet there …

知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。

I am struggling to understand what the space $L^1$ is, and what it means for a function to be $L^1$. A friend told me that a function $f$ is $L^1$ if $\int_\mathbb {R} |f|$ is finite.

Jun 13, 2020 · Is there a formal proof for $(-1) \\times (-1) = 1$? It's a fundamental formula not only in arithmetic but also in the whole of math. Is there a proof for it or is it just assumed?

@申力立 的证明存在错误，错误在于显然地认为 0.99\cdots 9\ (n\text {个}9)\ <0.999\cdots\leq 1 成立，他的理由是从高到低依次比较每一位数字的大小，但这并不是显然的，这一性质是在已经定义好了 …

Apr 25, 2013 · The examples given with base 10 and 2 in the question are positional bases. In a positional base 1, you only got one digit, with no value: 0. All positions will have zero value, and you …

比如，用质数组合得到数字6的唯一方法是2×3（顺序不重要，所以3×2算是同一种方法）。 然而，如果我们说1也算质数的话，那么得到6的方法就还有1×2×3和1×1×2×3，等等。 1的存在会破坏一切，对我 …

May 11, 2015 · There are multiple ways of writing out a given complex number, or a number in general. Usually we reduce things to the "simplest" terms for display -- saying $0$ is a lot cleaner than saying …

把1英寸分成8等分: 1/8 1/4 3/8 1/2 5/8 3/4 7/8 英寸。 This is an arithmetic sequence since there is a common difference between each term. In this case, adding 18 to the previous term in the sequence …