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I've noticed this matrix product pop up repeatedly and can't seem to de. 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 number very close to 1 to a large power can be anything. It's a fundamental formula not only in arithmetic but also in the whole of math 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 definition of complex exponentiation, although it is an immediate consequence of the definition of natural number exponentiation.

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。 Intending on marking as accepted, because i'm no mathematician and this response makes sense to a commoner However, i'm still curious why there is 1 way to permute 0 things, instead of 0 ways. 49 actually 1 was considered a prime number until the beginning of 20th century

Unique factorization was a driving force beneath its changing of status, since it's formulation is quickier if 1 is not considered a prime But i think that group theory was the other force. 实际上，天气预报中所说的雨量跟公众了解的积水深度并不能完全等同。 气象上一般把连续24小时，降水量50毫米以上的雨叫暴雨。 我们先以1毫米降水为例，看看小雨的威力。 首先，1毫米雨，看上去微乎其微，但如果降雨的范围（面积）很大，雨量也很可观。 How do i convince someone that $1+1=2$ may not necessarily be true

I once read that some mathematicians provided a very length proof of $1+1=2$

Can you think of some way to 两边求和，我们有 ln (n+1)<1/1+1/2+1/3+1/4+……+1/n 容易的， \lim _ {n\rightarrow +\infty }\ln \left ( n+1\right) =+\infty ，所以这个和是无界的，不收敛。

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