query: Proof that $\sqrt{x}=-\sqrt{x}$
positive_passages.docid: 6650
positive_passages.text: Why $\sqrt{-1 \times -1} \neq \sqrt{-1}^2$?
negative_passages.docid: 37723
negative_passages.text: Proof that $-(-x) = x$ using just the field axioms
negative_passages.docid: 2072
negative_passages.text: Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
negative_passages.docid: 157847
negative_passages.text: If $x_n \to 0$, show that $\sqrt{x_n} \to 0$
negative_passages.docid: 13899
negative_passages.text: Proof that $-v = (-1)*v$
negative_passages.docid: 78463
negative_passages.text: Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
negative_passages.docid: 67605
negative_passages.text: Different proof that $\sqrt{2}$ is irrational
negative_passages.docid: 62485
negative_passages.text: How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
negative_passages.docid: 88425
negative_passages.text: Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
negative_passages.docid: 36697
negative_passages.text: Proving that $\int_{-b}^{-a}f(-x)dx=\int_{a}^{b}f(x)dx$
negative_passages.docid: 133496
negative_passages.text: is $\sqrt{x}$ always positive?
negative_passages.docid: 110661
negative_passages.text: When does $\sqrt{a b} = \sqrt{a} \sqrt{b}$?
negative_passages.docid: 107765
negative_passages.text: Prove that there exists two roots in $[-1,1]$
negative_passages.docid: 5347
negative_passages.text: Using the definition of a vector space to prove that $0x = 0$ and $(-1)x = -x$
negative_passages.docid: 108429
negative_passages.text: Show that if $x_n \to x$ then $\sqrt{x_n} \to \sqrt{x}$
negative_passages.docid: 154945
negative_passages.text: $|px^2+qx+r|\le1$ for all $x$ in $[-1; 1]$, show that $|rx^2+qx+p|\le2$ for all $x$ in $[-1; 1]$
negative_passages.docid: 150738
negative_passages.text: Proof of $(A - B) - C = A - (B \cup C)$