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?

Possible Duplicate: Prove 0! = 1 0! = 1 from first principles Why does 0! = 1 0! = 1? All I know of factorial is that x! x! is equal to the product of all the numbers that come before it. The product of 0 and …

Feb 3, 2021 · So that's the "proof". The failure is at step 5, where you say that pq = pr p q = p r implies that q = r q = r; that's true only if you know p p is nonzero. For instance 0 ⋅ 5 = 0 ⋅ 7 0 5 = 0 7, but that …

How do I calculate this sum in terms of 'n'? I know this is a harmonic progression, but I can't find how to calculate the summation of it. Also, is it an expansion of any mathematical function? 1 ...

How can I prove from first principles that $0!$ is equal to $1$?

Nov 28, 2019 · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant …

Aug 17, 2014 · Prove it for n=1; then, assuming that it is true for n=k, try to show that it is true for n=k+1. It is easy indeed. (I do not know the name of this proving method.)

May 9, 2018 · 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？

May 11, 2015 · Why is 1/i 1 / i equal to −i i? Ask Question Asked 10 years, 8 months ago Modified 1 year, 1 month ago Viewed 116k times

Aug 24, 2016 · 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.