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  • arithmetic - Formal proof for $ (-1) \times (-1) = 1$ - Mathematics . . .
    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?
  • 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
  • Why is $1$ not a prime number? - Mathematics Stack Exchange
    If 1 is defined to be a prime number, then we'd have to change that theorem to: "every positive integer can be written uniquely as a product of primes, except for infinite multiplications by 1" So we choose to go with the easier path of defining 1 to not be a prime
  • 首页 - 知乎
    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。
  • Why is $1 i$ equal to $-i$? - Mathematics Stack Exchange
    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 While $1 i = i^ {-1}$ is true (pretty much by definition
  • 数字1的本质是什么？ - 知乎
    数字1的本质就是对各个文明表示1的符号和文字的再次抽象，因其简洁性而被广泛接受。 1，1的发现，各文明在其打猎和其他劳动中因为分配产生计数的需要，从而在语言中创造出数字，进而创造出文字直到专用的数字符号1。这个需要当你面对一些水果进而分给几个人的时候是显然存在的，甚至当你
  • 1-1+1-1+1-1+1. . . 这个无穷数列的值是什么？如何证明？ - 知乎
    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。
  • False Proof of 1=-1 - Mathematics Stack Exchange
    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
  • 如何定义什么是 1？ - 知乎
    我们可以从数学上证明 1+1=2，但是如何定义 1 是什么。如果说是 0 的后继数，那又如何定义 0 呢？
  • algebra precalculus - Prove $0! = 1$ from first principles . . .
    How can I prove from first principles that $0!$ is equal to $1$?





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