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How do i convince someone that $1+1=2$ may not necessarily be true? Is there a proof for it or is it just assumed? I've noticed this matrix product pop up repeatedly.

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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.

A reason that we do define $0!$ to be. The theorem that $\binom {n} {k} = \frac {n!} {k! I once read that some mathematicians provided a very length proof of $1+1=2$. 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。

It's a fundamental formula not only in arithmetic but also in the whole of math. Or, why is the definition of prime numbers given for integers greater than $1$?