query: Why $x$ cannot be zero in $y=\frac{1}{\frac{1}{x}}$
positive_passages.docid: 146770
positive_passages.text: Why is $\frac{1}{\frac{1}{0}}$ undefined?
negative_passages.docid: 136782
negative_passages.text: Prove that $x * y = \frac{x+y}{1+xy}$ is a stable part of $G=(-1, 1)$
negative_passages.docid: 110126
negative_passages.text: Prove that $\lim\limits_{(x,y) \to (0,0)} \frac{{x{y^2}}}{{{x^2} + {y^4}}} = 0$
negative_passages.docid: 64941
negative_passages.text: Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real?
negative_passages.docid: 71802
negative_passages.text: $x + \frac1y = y + \frac1z = z + \frac1x$, then value of $xyz$ is?
negative_passages.docid: 34762
negative_passages.text: Why isn't $\int \frac{1}{x}~dx = \frac{x^0}{0}$?
negative_passages.docid: 10068
negative_passages.text: $f(x,y)= e^{-\frac{1}{x^2+y^2}}$ when $(x,y)\neq (0,0)$ and $f(0,0)=0$.
negative_passages.docid: 78786
negative_passages.text: Why does an open interval NOT have measure zero?
negative_passages.docid: 102019
negative_passages.text: How to solve inequality $1-\frac{1}{x}\geq 0$ correctly?
negative_passages.docid: 121085
negative_passages.text: Showing that $\lim\limits_{x \rightarrow 0} \frac{1}{x}$ does not exist.
negative_passages.docid: 112709
negative_passages.text: $\frac{1}{x-a} + \frac{1}{x-b} + \frac{1}{x-c} = 0 $ has precisely two real roots
negative_passages.docid: 68990
negative_passages.text: Show that $\frac 1{1+x+y^{-1}}+\frac1{1+y+z^{-1}}+\frac1{1+z+x^{-1}}=1$ if $xyz=1$
negative_passages.docid: 80720
negative_passages.text: What paths to choose to prove that $\lim_{(x,y) \to (0,0)}\frac{xy^2}{x^2 - y^2}$ does not exist?
negative_passages.docid: 84987
negative_passages.text: Two paths that show that $\frac{x-y}{x^2 + y^2}$ has no limit when $(x,y) \rightarrow (0,0)$
negative_passages.docid: 150601
negative_passages.text: The limit of $\sin(1/x)$ as $x\to 0$ does not exists
negative_passages.docid: 62606
negative_passages.text: Non-existence of $\lim \limits_{(x, y) \to (0,0)} \frac{x^3 + y^3}{x - y} $
negative_passages.docid: 13150
negative_passages.text: If the derivative of $f$ is never zero, then $f$ is one-to-one