query: Prove that the set of positive rational values that are less than $ \sqrt{2}$ has no maximum value
positive_passages.docid: 62224
positive_passages.text: Need help with proof for Dedekind cuts on $\mathbb{Q}^+$
negative_passages.docid: 9966
negative_passages.text: Range of a Rational Function
negative_passages.docid: 148582
negative_passages.text: Proof: $\|X\|_2\leq \sqrt{n}\|X\|_\infty$
negative_passages.docid: 75639
negative_passages.text: Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
negative_passages.docid: 2408
negative_passages.text: Show that a polynomial has at least one positive solution/root.
negative_passages.docid: 51687
negative_passages.text: Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
negative_passages.docid: 56818
negative_passages.text: Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
negative_passages.docid: 31295
negative_passages.text: $x+y\sqrt{2}$ infimum ($x,y\in \mathbb{Z}$)
negative_passages.docid: 140817
negative_passages.text: Real Analysis Inequality Proof Involving Reals and Rationals $0 < |r - q| < \varepsilon$
negative_passages.docid: 24683
negative_passages.text: For i.i.d. $\{X_n\}$ proving $\frac1n\max\limits_{1\leqslant k\leqslant n}|X_k|\xrightarrow{\mathrm{a.s.}}0\Leftrightarrow E(|X_1|)<+∞$
negative_passages.docid: 75012
negative_passages.text: Additive group of rationals has no minimal generating set
negative_passages.docid: 67605
negative_passages.text: Different proof that $\sqrt{2}$ is irrational
negative_passages.docid: 84558
negative_passages.text: Prove that the square root of a positive integer is either an integer or irrational
negative_passages.docid: 80920
negative_passages.text: Prove or disprove: For any $v\in\mathbb{R}^n, \|v\|_1\|v\|_\infty \leq \frac{1+\sqrt{n}}{2}\|v\|_2^2$
negative_passages.docid: 118244
negative_passages.text: An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
negative_passages.docid: 105768
negative_passages.text: Proof involving absolute value and maximums
negative_passages.docid: 100862
negative_passages.text: Polynomials with rational zeros