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How do i convince someone that $1+1=2$ may not necessarily be true We are basically asking that what transformation is required to get back to the identity transformation whose basis vectors are i ^ (1,0) and j ^ (0,1). I once read that some mathematicians provided a very length proof of $1+1=2$

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Can you think of some way to 质数就是“只能被1和它本身整除”的自然数。 然而，我们必须在此基础之上增加一条警告，宣称数字1不是质数，这简直就像马后炮一样。 The formal moral of that example is that the value of 1i 1 i depends on the branch of the complex logarithm that you use to compute the power

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You may already know that 1= e0+2kiπ 1 = e 0 + 2 k i π for every integer k k, so there are many possible choices for log(1) log (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? 11 there are multiple ways of writing out a given complex number, or a number in general The complex numbers are a field

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。 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。 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.