Question

Show that $S=\operatorname{span}\{v^{(i,j)},\;1\leq i\neq j\leq n\}.$

score 30 · Answer 1 · 2026-04-16 04:13:54

30

Views

Show that $S=\operatorname{span}\{v^{(i,j)},\;1\leq i\neq j\leq n\}.$

Published on 16 Apr 2026 - 4:13

score 222 · Answer 2 · 2026-05-07 12:18:57

222

Views

Does an integral inequality imply a pointwise inequality?

Published on 07 May 2026 - 12:18

score 1.3k · Answer 3 · 2026-05-10 16:57:17

1.3k

Views

Proving lim sup of a sequence of measurable functions is measurable

Published on 10 May 2026 - 16:57

score 109 · Answer 4 · 2026-04-15 17:12:29

109

Views

Prove that if $f$ differentiable in $x^$ and $f(x^)=0$, then $\liminf_{x\to x^}\frac{|f(x)|}{||x-x^||}=0$ if $n>1$

Published on 15 Apr 2026 - 17:12

score 449 · Answer 5 · 2026-04-16 21:20:18

449

Views

Given that $\lim\limits_{n \to \infty}\left(1+\frac{1}{n}\right)^n=e$, show that $1+\frac{1}{1!}+\frac{1}{2!}+\cdots=e$.

Published on 16 Apr 2026 - 21:20

score 144 · Answer 6 · 2026-04-16 04:45:58

144

Views

Is $\limsup |C_n|^{\frac{1}{n}} = \limsup |C_{n+j}|^{\frac{1}{n}}? $ where $j\geq0 $

Published on 16 Apr 2026 - 4:45

score 55 · Answer 7 · 2026-04-17 11:21:33

What are the limit points of set $E=\left\{ a_{n}\::\:n=1,\:2,\:3,\:\cdots\right\} $, $a_{n}=\frac{n-1}{n+1}\left|\sin\frac{n\pi}{7}\right|$

score 855 · Answer 8 · 2026-05-10 15:02:41

855

Views

Show that there is a continuous real function $h$ on $[0,1]$ such that $\lim \sup |\frac{h(x+t)-h(x)}{t}| = \infty$ for all $x \in [0,1)$

Published on 10 May 2026 - 15:02

score 50 · Answer 9 · 2026-04-30 10:19:39

50

Views

Easy Lim Sup Proof?

Published on 30 Apr 2026 - 10:19

score 117 · Answer 10 · 2026-04-15 03:03:01

Doubt about step of the proof that $\limsup\limits_{n\to\infty}\left|\sum\limits_{\ell=1}^mz^n_\ell\right|^{1/n}=\max\limits_{1\le\ell\le m}|z_\ell|$

score 257 · Answer 11 · 2026-04-10 08:58:48

257

Views

How to prove an average inequality about limsup\liminf

Published on 10 Apr 2026 - 8:58

score 112 · Answer 12 · 2026-04-15 05:21:39

112

Views

Finding $f$ satisfies $\limsup_{n\to\infty}\frac{\tau(n)}{f(n)}=1$

Published on 15 Apr 2026 - 5:21

score 1.2k · Answer 13 · 2026-04-13 04:48:01

1.2k

Views

How to find the limsup and liminf of a sequence of intervals

Published on 13 Apr 2026 - 4:48

score 420 · Answer 14 · 2026-05-10 17:18:07

420

Views

Explanation of $\lim\sup$ of a sequence of random variables in measure theory

Published on 10 May 2026 - 17:18

score 175 · Answer 15 · 2026-04-15 15:54:29

175

Views

Probability of events tends to zero implies probabilty of liminf is zero

Published on 15 Apr 2026 - 15:54

List Question

Show that $S=\operatorname{span}\{v^{(i,j)},\;1\leq i\neq j\leq n\}.$

Does an integral inequality imply a pointwise inequality?

Proving lim sup of a sequence of measurable functions is measurable

Prove that if $f$ differentiable in $x^$ and $f(x^)=0$, then $\liminf_{x\to x^}\frac{|f(x)|}{||x-x^||}=0$ if $n>1$

Given that $\lim\limits_{n \to \infty}\left(1+\frac{1}{n}\right)^n=e$, show that $1+\frac{1}{1!}+\frac{1}{2!}+\cdots=e$.

Is $\limsup |C_n|^{\frac{1}{n}} = \limsup |C_{n+j}|^{\frac{1}{n}}? $ where $j\geq0 $

What are the limit points of set $E=\left\{ a_{n}\::\:n=1,\:2,\:3,\:\cdots\right\} $, $a_{n}=\frac{n-1}{n+1}\left|\sin\frac{n\pi}{7}\right|$

Show that there is a continuous real function $h$ on $[0,1]$ such that $\lim \sup |\frac{h(x+t)-h(x)}{t}| = \infty$ for all $x \in [0,1)$

Easy Lim Sup Proof?

Doubt about step of the proof that $\limsup\limits_{n\to\infty}\left|\sum\limits_{\ell=1}^mz^n_\ell\right|^{1/n}=\max\limits_{1\le\ell\le m}|z_\ell|$

How to prove an average inequality about limsup\liminf

Finding $f$ satisfies $\limsup_{n\to\infty}\frac{\tau(n)}{f(n)}=1$

How to find the limsup and liminf of a sequence of intervals

Explanation of $\lim\sup$ of a sequence of random variables in measure theory

Probability of events tends to zero implies probabilty of liminf is zero

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