query: Is $(x+1)/(x^2-1)$ defined for $x=-1$?
positive_passages.docid: 49368
positive_passages.text: Why does factoring eliminate a hole in the limit?
negative_passages.docid: 113386
negative_passages.text: Find all integer roots of: $x^2(y-1)+y^2(x-1)=1$
negative_passages.docid: 53866
negative_passages.text: Prove $ x^n-1=(x-1)(x^{n-1}+x^{n-2}+...+x+1)$
negative_passages.docid: 6650
negative_passages.text: Why $\sqrt{-1 \times -1} \neq \sqrt{-1}^2$?
negative_passages.docid: 106911
negative_passages.text: Square root of $-1$ in the ring $\mathbb{R}[x]/\langle(x^2+1)^2\rangle$
negative_passages.docid: 96554
negative_passages.text: Why is $x^0 = 1$ except when $x = 0$?
negative_passages.docid: 49372
negative_passages.text: $x+1/x$ an integer implies $x^n+1/x^n$ an integer
negative_passages.docid: 51769
negative_passages.text: If $x,y,z\in[-1,1]$ and $1+2xyz\geq x^2+y^2+z^2$, then can we infer $1+2(xyz)^n\geq x^{2n}+y^{2n}+z^{2n}$?
negative_passages.docid: 94499
negative_passages.text: What is $c + (-c)$?
negative_passages.docid: 14150
negative_passages.text: Zero to the zero power – is $0^0=1$?
negative_passages.docid: 84597
negative_passages.text: Derivative of $(1-x)^{-2}$
negative_passages.docid: 60261
negative_passages.text: Is $\sqrt{x^2}=|x|$ or $=x$? Isn't $(x^2)^\frac12=x?$
negative_passages.docid: 144765
negative_passages.text: Solving $\sqrt{x+5} = x - 1$
negative_passages.docid: 41645
negative_passages.text: Checking my understanding: $1 - 1 + 1 - 1 + 1 - ... = \frac{1}{2}$
negative_passages.docid: 82097
negative_passages.text: If $A \succeq B$, is it true that $B^{-1} \succeq A^{-1}$?
negative_passages.docid: 35556
negative_passages.text: $f(z)=\frac{z}{1+|z|} $ Is 1-1?
negative_passages.docid: 155285
negative_passages.text: difficulty of accepting $i^2 = -1$ for first timers