query: Is there a way to show R2(s + 1, t + 1) > s · t .
positive_passages.docid: 152838
positive_passages.text: Relation between Ramsey Numbers: $R(s, t) > (t-1)(s-1)$
negative_passages.docid: 106609
negative_passages.text: Show that $e^{iy} = 1 + iy + \frac{\mu_1 y^2}{2}$ for all $y \in \mathbb{R}$ with $|\mu_1| \leq 1$
negative_passages.docid: 149801
negative_passages.text: prove that $TS = ST$
negative_passages.docid: 110643
negative_passages.text: What are the strategies I can use to prove $f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$?
negative_passages.docid: 19424
negative_passages.text: Showing $(M^\perp)^\perp=\overline{M}$
negative_passages.docid: 79040
negative_passages.text: Graph of $|x| + |y| = 1$
negative_passages.docid: 59872
negative_passages.text: How to prove $\inf(S)=-\sup(-S)$?
negative_passages.docid: 101699
negative_passages.text: Equivalent of Maple `ShowSolution` command in *Matematica*
negative_passages.docid: 98824
negative_passages.text: linear transformation $T$ such that $TS = ST$
negative_passages.docid: 99483
negative_passages.text: If $T(n+1)=T(n)+\lfloor \sqrt{n+1}, \rfloor$ $\forall n\geq 1$, what is $T(m^2)$?
negative_passages.docid: 142360
negative_passages.text: How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
negative_passages.docid: 63155
negative_passages.text: Express $1+2\cos a$ as a product
negative_passages.docid: 115533
negative_passages.text: Inequality for small values of $t$
negative_passages.docid: 33196
negative_passages.text: show that A(T) is a group under operation of composition of functions
negative_passages.docid: 35611
negative_passages.text: How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$?
negative_passages.docid: 135747
negative_passages.text: Prove $x^{rs}-1=(x^s-1)(x^{s(r-1)}+...+x^s+1)$
negative_passages.docid: 80095
negative_passages.text: Show $|a|+|b|+|c|+|a+b+c| \geq  |a+b|+|b+c|+|c+a|$ for complex $a$, $b$, $c$