- Why is $1 i$ equal to $-i$? - Mathematics Stack Exchange
While 1 i = i−1 1 i = i 1 is true (pretty much by definition), if we have a value c c such that c∗i = 1 c ∗ i = 1 then c= i−1 c = i 1 This is because we know that inverses in the complex numbers are unique
- What is the value of $1^i$? - Mathematics Stack Exchange
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
- Formal proof for $ (-1) \times (-1) = 1$ - Mathematics Stack Exchange
Is there a formal proof for $(-1) \\times (-1) = 1$? 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?
- abstract algebra - Prove that 1+1=2 - Mathematics Stack Exchange
Possible Duplicate: 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
- Word，插入多级列表，但是改了1. 1，第二章的2. 1也变成1. 1，随着改变而改变，这种情况怎么处? - 知乎
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
- factorial - Why does 0! = 1? - Mathematics Stack Exchange
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
- algebra precalculus - Prove $0! = 1$ from first principles . . .
How can I prove from first principles that $0!$ is equal to $1$?
- Arithmetic pattern $1 + 2 = 3$, $4 + 5 + 6 = 7 + 8$, and so on
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 terms on the right This should let you determine a formula like the one you want Then prove it by induction
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