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11 there are multiple ways of writing out a given complex number, or a number in general 1 indeed what you are proving is that in the complex numbers you don't have (in general) $$\sqrt {xy}=\sqrt {x}\sqrt {y}$$ because you find a counterexample. The complex numbers are a field

There are infinitely many possible values for $1^i$, corresponding to different branches of the complex logarithm Then prove it by induction. 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.

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 We treat binomial coefficients like $\binom {5} {6}$ separately already 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? 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.

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 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

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

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