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11 there are multiple ways of writing out a given complex number, or a number in general 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。 The complex numbers are a field
It's a fundamental formula not only in arithmetic but also in the whole of math We treat binomial coefficients like $\binom {5} {6}$ separately already Is there a proof for it or is it just assumed?
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 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。 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。 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 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. The theorem that $\binom {n} {k} = \frac {n!} {k Otherwise this would be restricted to $0 <k < n$ A reason that we do define $0!$ to be $1$ is so that we can cover those edge cases with the same formula, instead of having to treat them separately
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