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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。 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 $1+1=2$ 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. 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? 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. 11 there are multiple ways of writing out a given complex number, or a number in general 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。 知乎是一个中文互联网高质量问答社区和创作者聚集的原创内容平台,提供知识共享、互动交流和个人成长机会。 But i'm not sure, if my proof is correct, because i'm not very experienced