query: Show $\inf (f_n )=- \sup (-f_n)$
positive_passages.docid: 27482
positive_passages.text: How to show $-\sup(-A)=\inf(A)$?
negative_passages.docid: 75317
negative_passages.text: Show that $(s_n)$ is a Cauchy sequence
negative_passages.docid: 75373
negative_passages.text: Show that $2^n>n$ for $n\in \mathbb{N}$
negative_passages.docid: 88278
negative_passages.text: Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective
negative_passages.docid: 59475
negative_passages.text: Show that $\sqrt{n+1}-\sqrt{n}\to0$
negative_passages.docid: 138026
negative_passages.text: To show that $n!f(x) \in \mathbb{Z}[x]$
negative_passages.docid: 102553
negative_passages.text: How to show that $f(z) = f(i)$
negative_passages.docid: 57639
negative_passages.text: Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
negative_passages.docid: 14162
negative_passages.text: How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$
negative_passages.docid: 23071
negative_passages.text: Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$
negative_passages.docid: 19457
negative_passages.text: Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
negative_passages.docid: 88147
negative_passages.text: Show that $g_n(x)=nf(x+1/n)-nf(x)$ converges uniformly to $f'$
negative_passages.docid: 37906
negative_passages.text: Prove $s_n$ is a Cauchy sequence for $|s_{n+1}-s_n|\lt2^{-n}$
negative_passages.docid: 131692
negative_passages.text: How to show that $f_{0}f_{1}+f_{1}f_{2}+...+f_{2n-1}f_{2n} = f^{2}_{2n}$
negative_passages.docid: 11322
negative_passages.text: Show that $f$ vanishes identically.
negative_passages.docid: 117640
negative_passages.text: Prove that $\lim \inf \dfrac{x_{n+1}}{x_n}\leq \lim \inf x_n^{1\over n} \leq \lim \sup x_n^{1\over n} \leq \lim \sup \dfrac{x_{n+1}}{x_n}. $
negative_passages.docid: 20467
negative_passages.text: Show that $(y_n)\in l^q$