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1 1 additional practice operations on real numbers

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5 min read · Apr 22, 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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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?

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) …

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 …

总体上，GLM-5.1 这一代大幅扩展了编程的适应范围，不再是前端only战神，也不只是oneshot 样子货，是可以在复杂工况下充当编程主力。但要注意在超长上下文时，容易幻觉爆炸，如果遇到2轮改不 …

Aug 30, 2010 · There are infinitely many possible values for $1^i$, corresponding to different branches of the complex logarithm. The confusing point here is that the formula $1^x = 1$ is not part of the …