query: Prove that $-1 \cdot x=-x$
positive_passages.docid: 111515
positive_passages.text: Proving that $-a=(-1)\cdot a$
negative_passages.docid: 116856
negative_passages.text: Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
negative_passages.docid: 155769
negative_passages.text: Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n-1}$ using the binomial theorem for $n\geq1$
negative_passages.docid: 116356
negative_passages.text: Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$
negative_passages.docid: 89637
negative_passages.text: Proof that in a field $x=0$ is equivalent to $x=-x$
negative_passages.docid: 69515
negative_passages.text: If $x_n\cdot y_n\to 0$ then $x_n \to 0$ or $y_n \to 0 $
negative_passages.docid: 34299
negative_passages.text: Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$
negative_passages.docid: 57780
negative_passages.text: $\sum_{i=1}^n i\cdot i! = (n+1)!-1$ By Induction
negative_passages.docid: 78736
negative_passages.text: Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
negative_passages.docid: 103801
negative_passages.text: $xT=x$ iff $x=e$ implies that every $g$ may be written as $x^{-1}(xT)$ for some $x\in G$.
negative_passages.docid: 87848
negative_passages.text: Formal proof for $(-1) \times (-1) = 1$
negative_passages.docid: 95057
negative_passages.text: Possible fake proof of $1= -1$
negative_passages.docid: 55094
negative_passages.text: How to show $i^{-1} = -i$?
negative_passages.docid: 53866
negative_passages.text: Prove $ x^n-1=(x-1)(x^{n-1}+x^{n-2}+...+x+1)$
negative_passages.docid: 52750
negative_passages.text: Prove that $f^\ast\omega=\det f \cdot \omega$
negative_passages.docid: 33030
negative_passages.text: Proof that $\inf A = -\sup(-A)$
negative_passages.docid: 151646
negative_passages.text: Prove by induction that $\sum_{i=1}^{n} i \cdot 2^i = (n-1) \cdot 2^{n+1} +2$. Help finding my mistake