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  • Why is $1 i$ equal to $-i$? - Mathematics Stack Exchange
    11 There are multiple ways of writing out a given complex number, or a number in general Usually we reduce things to the "simplest" terms for display -- saying $0$ is a lot cleaner than saying $1-1$ for example The complex numbers are a field This means that every non-$0$ element has a multiplicative inverse, and that inverse is unique
  • 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?
  • 知乎 - 有问题，就会有答案
    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。
  • 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
  • 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
  • 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
  • If $A A^{-1} = I$, does that automatically imply $A^{-1} A = I$?
    This is same as AA -1 It means that we first apply the A -1 transformation which will take as to some plane having different basis vectors If we think what is the inverse of A -1 ? 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)
  • 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
  • 1 1+1 2+1 3+1 4+……+1 n=？怎么个解法？ - 知乎
    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。
  • False Proof of 1=-1 - Mathematics Stack Exchange
    False Proof of 1=-1 [duplicate] Ask Question Asked 9 years, 3 months ago Modified 9 years, 3 months ago





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