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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? 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 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.

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).

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 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. The other interesting thing here is that 1,2,3, etc

Appear in order in the list And you have 2,3,4, etc Terms on the left, 1,2,3, etc This should let you determine a formula like the one you want

Then prove it by induction.

The reason why $1^\infty$ is indeterminate, is because what it really means intuitively is an approximation of the type $ (\sim 1)^ {\rm large \, number}$ And while $1$ to a large power is 1, a number very close to 1 to a large power can be anything. This sum is called $h_n$ the $n$thharmonic number and has no known closed form.

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