Jun 28, 2022 · 50 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 …

Jun 13, 2020 · 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?

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 …

Dec 2, 2024 · What is the expansion for $(1-x)^{-n}$? Could find only the expansion upto the power of $-3$. Is there some general formula?

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

Aug 17, 2014 · 13 So what I am trying to prove is for any real number x and natural number n, prove xn − 1 = (x − 1)(xn−1 +xn−2 + ⋯ + x + 1) x n 1 = (x 1) (x n 1 + x n 2 + + x + 1) I think that to prove this I …

Oct 27, 2016 · There is a general formula for indeterminate form 1∞ 1 ∞ which I'm looking for a proof which is also used here. (picture) Given

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？