query: Proof of "if $x<y$, then $xz<yz$"
positive_passages.docid: 23869
positive_passages.text: Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive
negative_passages.docid: 110495
negative_passages.text: $X_n \to X, Y_n \to c$ in distribution implies $X_n Y_n \to Xc$ in distribution
negative_passages.docid: 16948
negative_passages.text: Need help with a proof that if $xy=0$ then $x=0$ or $y=0$
negative_passages.docid: 143072
negative_passages.text: Proving $|\sin x - \sin y| < |x - y|$
negative_passages.docid: 43246
negative_passages.text: Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
negative_passages.docid: 7775
negative_passages.text: Show that $|x-y|\leq |x|+|y|$.
negative_passages.docid: 135694
negative_passages.text: Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
negative_passages.docid: 46383
negative_passages.text: If $x$ divides $z$, $y$ divides $z$ and $x$ and $y$ are relatively prime, then $xy$ divides $z$.
negative_passages.docid: 144372
negative_passages.text: How to Prove that if $A$ is bounded, then $A \cdot A$ is bounded?
negative_passages.docid: 106799
negative_passages.text: Proof Verification: Converse of Intermediate Value Theorem
negative_passages.docid: 105367
negative_passages.text: Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
negative_passages.docid: 142631
negative_passages.text: Show that A has the same cardinality as $A\setminus\{x,y,z\}$
negative_passages.docid: 136427
negative_passages.text: Given $∃y.∀x.p(x,y)$, use the Fitch system to prove $∀x.∃y.p(x,y)$
negative_passages.docid: 138632
negative_passages.text: Proof that if $a > 0$, then $\frac{1}{a} > 0$ using just field and order axioms
negative_passages.docid: 28822
negative_passages.text: $|x| - |y| \leq |x-y|?$
negative_passages.docid: 29679
negative_passages.text: Prove: $|x-y|\leq |x|+|y|$
negative_passages.docid: 52614
negative_passages.text: (exercise from Tao's analysis book) Proof of a lemma relating to power set of X