query: Counter example to show that $ s(X) \le d(X) $
positive_passages.docid: 16550
positive_passages.text: Is $ d(X) \le s(X)? $
negative_passages.docid: 147661
negative_passages.text: Show that {$x_n$} is a convergent sequence if $d(x_{n+2}, x_{n+1})≤ rd(x_{n+1}, x_n)$
negative_passages.docid: 106767
negative_passages.text: $|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
negative_passages.docid: 144589
negative_passages.text: Proving that if $f(x) \le g(x)$ then $f(x_0) \le g(x_0)$
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: 76347
negative_passages.text: Shorter proof for some equvalences
negative_passages.docid: 106585
negative_passages.text: Show $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$.
negative_passages.docid: 138931
negative_passages.text: Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
negative_passages.docid: 2907
negative_passages.text: How do I show that $x$ is a root of $p(x)$ in $F[x]/\langle p(x)\rangle$?
negative_passages.docid: 104263
negative_passages.text: How to show that $f'(x)<2f(x)$
negative_passages.docid: 119735
negative_passages.text: Show that $\mathbb{E}(g(T-p)) < \mathbb{E}(g(S-p))$ for any convex function $g$ if $T$ and $S$ are estimators of $p$
negative_passages.docid: 16253
negative_passages.text: Proof that $|\sin(nx)| \le n|\sin(x)|$
negative_passages.docid: 43376
negative_passages.text: If $A$ is compact and $B$ is closed, show $d(A,B)$ is achieved
negative_passages.docid: 151958
negative_passages.text: How to show $f'(0)$ exist and is equal to $1$?
negative_passages.docid: 76292
negative_passages.text: Showing that $f$ is identically $0$ on $\mathbb{D}$
negative_passages.docid: 101286
negative_passages.text: How show that $|a_{n}-1|\le c\lambda ^n,\lambda\in (0,1)$
negative_passages.docid: 139537
negative_passages.text: Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.