query: Discrete math statement $\rightarrow$ plain English. $\left(Longer\right)$
positive_passages.docid: 157924
positive_passages.text: $\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
negative_passages.docid: 39405
negative_passages.text: Symmetric difference = Ø
negative_passages.docid: 153450
negative_passages.text: \xRightarrow (text)
negative_passages.docid: 113406
negative_passages.text: How does the right-shift operator work in a python print statement?
negative_passages.docid: 28687
negative_passages.text: Efficient bitwise operations for counting bits or find the right|left most ones
negative_passages.docid: 58239
negative_passages.text: Symbols for left and right limits
negative_passages.docid: 92492
negative_passages.text: Natural Deduction: $(p \lor q)\to r\vdash p \to r$ and $p\to\neg q\leftrightarrow(r\lor s),\neg s\vdash (p\land \neg q)\to r$
negative_passages.docid: 132068
negative_passages.text: Write the set $\{1, 6, 11, 16,\ldots\}$ in compact (concise) notation.
negative_passages.docid: 27610
negative_passages.text: Given the permutation $\sigma=\left(\begin{array}{ccccc} 1&2&3&4&5\\ 3&1&2&5&4 \end{array}\right)$
negative_passages.docid: 58561
negative_passages.text: Right and left inverse
negative_passages.docid: 142815
negative_passages.text: Is Left associativity only for Postfix expression?
negative_passages.docid: 155051
negative_passages.text: Writing $\left(\mathbf Z/2\oplus\mathbf Z/4\oplus\mathbf Z/8\right)\oplus\left(\mathbf Z/9\oplus\mathbf Z/27\right)$ in a different way
negative_passages.docid: 5789
negative_passages.text: $ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$
negative_passages.docid: 84433
negative_passages.text: Expression generating $\left( \frac{3}{10}, \, \frac{3}{10} + \frac{33}{100}, \, \frac{3}{10} + \frac{33}{100} + \frac{333}{1000}, \dots \right)$
negative_passages.docid: 4730
negative_passages.text: How can I pad an integer with zeros on the left?
negative_passages.docid: 78191
negative_passages.text: Define $\|\cdot\| \colon V \rightarrow \mathbb{R} $ by $\|a\| =\sum 2^n |a_n| $, then choose the correct option
negative_passages.docid: 137614
negative_passages.text: $\left|\frac{x}{|x|}-\frac{y}{|y|}\right|\leq |x-y|$, for $|x|, |y|\geq 1$?