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1 year marathon training plan

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5 min read · Apr 21, 2026

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May 9, 2018 · 我们可以从数学上证明 1+1=2，但是如何定义 1 是什么。如果说是 0 的后继数，那又如何定义 0 呢？

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红线是n-1到n的割线，绿线是n处的切线图像上显然，割线的斜率大于切线的斜率。所以我们有割线的斜率 \dfrac {\ln \left ( n\right) -\ln \left ( n-1\right) } {n-\left ( n-1\right) } 大于切线的斜率 \left ( \ln n\right) …

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?

The reason why $1^\infty$ is indeterminate, is because what it really means intuitively is an approximation of the type $ (\sim 1)^ {\rm large \, number}$. And while $1$ to a large power is 1, a …

Aug 24, 2016 · 1 Indeed what you are proving is that in the complex numbers you don't have (in general) $$\sqrt {xy}=\sqrt {x}\sqrt {y}$$ Because you find a counterexample.

m = p 1 a 1 p 2 a 2 p 3 a 3 p n a n . 什么意思呢？它表示这样一个结论：对于任意的一个整数，你都能把它因数分解，而且结果是唯一的。举个例子：1001只能被分解成7×11×13，而且你再也找不到除 …

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 …