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How do i convince someone that $1+1=2$ may not necessarily be true 这个极限的推广形式 lim (x→0) (1+kx)^ (1/x) = e^k 也经常被使用。 这个极限的发现和研究在数学发展史上具有重要意义，它连接了离散与连续、代数与分析等多个数学领域，是理解指数增长和自然对数的基础。 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 In other words, an=a1+d (n−1) 11 there are multiple ways of writing out a given complex number, or a number in general

The complex numbers are a field

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? 注1：【】代表软件中的功能文字 注2：同一台电脑，只需要设置一次，以后都可以直接使用 注3：如果觉得原先设置的格式不是自己想要的，可以继续点击【多级列表】——【定义新多级列表】，找到相应的位置进行修改 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. 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。 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.

1/8 1/4 3/8 1/2 5/8 3/4 7/8 英寸。 this is an arithmetic sequence since there is a common difference between each term In this case, adding 18 to the previous term in the sequence gives the next term