Inf and sup on $A=\left\{(x_1,x_2,\dots,x_{10}) \in \mathbb R^{10}: \sum_{1 \le i<j \le 10} x_ix_j=45, x_1\ge0, x_2\ge 0,\dots, x_{10} \ge 0 \right\}$

score 56 · Answer 7 · 2023-05-28 20:42:39

56

Views

Infimum of the set $\{(1/m)^{1/n}+(1/n)^{1/m}\mid m,n\in\Bbb N\}$

Published on 28 May 2023 - 20:42

score 42 · Answer 8 · 2026-03-27 23:14:20

42

Views

Show that there exists $0 \neq v_0 \in H$ with $v_0 \perp V$ such that the supremum is attained.

Published on 27 Mar 2026 - 23:14

score 222 · Answer 9 · 2023-05-29 16:30:58

222

Views

Suppose function $f(x)$ is continuous on $[a,b]$ then the function $\sup_{a\le{t}\le{x}}f(t)$ is also continuous.

Published on 29 May 2023 - 16:30

score 202 · Answer 10 · 2026-03-30 04:58:43

202

Views

Proof of $\inf\left \{ \frac{\mathrm{d} (n^2)}{\mathrm{d} (n)} \; \bigg| \; n \in \mathbb{N} \right \}=0$, where $d(n)$ is the sum of digits of $n$

Published on 30 Mar 2026 - 4:58

score 45 · Answer 11 · 2023-05-30 19:40:50

45

Views

Is given statement indeed true?

Published on 30 May 2023 - 19:40

score 101 · Answer 12 · 2023-06-10 15:38:00

101

Views

Show $\bigcup\limits_{n\mid n\geq N}A_{n,m}=\left\{\sup\limits_{n\mid n\geq N}\left|\frac{S_n(\omega)}{n}-p\right|\geq\frac{1}{m}\right\}$

Published on 10 Jun 2023 - 15:38

score 57 · Answer 13 · 2023-06-11 14:06:50

57

Views

Is there a sequence $(t_n)_{n\ge 0}$ such that $\sup_n S_n < \infty$?

Published on 11 Jun 2023 - 14:06

score 141 · Answer 14 · 2023-06-11 15:15:19

141

Views

Is there a sequence $(t_n)_{n\ge 0}$ such that $\lim_n t_n = \infty$, $\lim_n \Delta_n = 0$ and $\sup_n S_n < \infty$?

Published on 11 Jun 2023 - 15:15

score 31 · Answer 15 · 2023-06-11 18:42:17

31

Views

Supremum of a function vs the infimum of its multiplicative version

Published on 11 Jun 2023 - 18:42

List Question

Let $S=\{\frac{x+1}{x^2+1}:x\in \mathbb{Q},x>0\}$ Prove that $\sup S=\frac{1+\sqrt{2}}{2}$

Definition od essential supremum for martingales with many measures

Find infimum and supremum of the function $f$ defined by the formula $f(x, y, z) = 2x+ 2y-3z$ on the set $A$

finding infimum of the ratio of largest to smallest distance of six points in $\mathbb R^2$

Find an upper bound for $\int_{0}^{1}\cos(x)\frac{x f'(x) - f(x) + f(0)}{x^2}dx$

Inf and sup on $A=\left\{(x_1,x_2,\dots,x_{10}) \in \mathbb R^{10}: \sum_{1 \le i<j \le 10} x_ix_j=45, x_1\ge0, x_2\ge 0,\dots, x_{10} \ge 0 \right\}$

Infimum of the set $\{(1/m)^{1/n}+(1/n)^{1/m}\mid m,n\in\Bbb N\}$

Show that there exists $0 \neq v_0 \in H$ with $v_0 \perp V$ such that the supremum is attained.

Suppose function $f(x)$ is continuous on $[a,b]$ then the function $\sup_{a\le{t}\le{x}}f(t)$ is also continuous.

Proof of $\inf\left \{ \frac{\mathrm{d} (n^2)}{\mathrm{d} (n)} \; \bigg| \; n \in \mathbb{N} \right \}=0$, where $d(n)$ is the sum of digits of $n$

Is given statement indeed true?

Show $\bigcup\limits_{n\mid n\geq N}A_{n,m}=\left\{\sup\limits_{n\mid n\geq N}\left|\frac{S_n(\omega)}{n}-p\right|\geq\frac{1}{m}\right\}$

Is there a sequence $(t_n)_{n\ge 0}$ such that $\sup_n S_n < \infty$?

Is there a sequence $(t_n)_{n\ge 0}$ such that $\lim_n t_n = \infty$, $\lim_n \Delta_n = 0$ and $\sup_n S_n < \infty$?

Supremum of a function vs the infimum of its multiplicative version

Trending Questions

Popular # Hahtags

Popular Questions