Question

Is $\emptyset$ bounded? Why then $\inf \emptyset = \infty$ is reasonable?

score 1.2k · Answer 1 · 2016-08-06 08:54:54

1.2k

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Is $\emptyset$ bounded? Why then $\inf \emptyset = \infty$ is reasonable?

Published on 06 Aug 2016 - 8:54

score 60 · Answer 2 · 2026-03-30 17:15:46

60

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Proof that $\lim\limits_{n\to\infty} \frac1{A_n}\sum_{k=1}^{n} { \mathbb{E} (a_k Y_k) } =0$.

Published on 30 Mar 2026 - 17:15

score 501 · Answer 3 · 2016-08-06 17:19:43

501

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how to determine the infimum of a multivariate function?

Published on 06 Aug 2016 - 17:19

score 419 · Answer 4 · 2016-08-07 00:45:32

419

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Supremum with respect to one variable is continuous (proof verification)

Published on 07 Aug 2016 - 0:45

score 208 · Answer 5 · 2026-03-27 23:46:34

208

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Proving $f(0) = 0, f(x) = \frac{1}{2^n}$ when $\frac{1}{2^{n+1}}<x<\frac{1}{2^n}$ is integrable

Published on 27 Mar 2026 - 23:46

score 115 · Answer 6 · 2016-08-13 18:57:29

115

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Domain monotonicity - $\mu_n (\Omega_2) \leq \mu_n (\Omega_1)$

Published on 13 Aug 2016 - 18:57

score 40 · Answer 7 · 2016-08-16 00:36:01

40

Views

Why must there exist a sequence $r_k ∈ R$ such that $r_k→r$?

Published on 16 Aug 2016 - 0:36

score 73 · Answer 8 · 2016-08-18 16:33:31

73

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Compute $\sup\limits_{x\in (0,2)}\left|\operatorname{cosh}\left(x^2-x-1\right)\right|$

Published on 18 Aug 2016 - 16:33

score 2.8k · Answer 9 · 2016-08-19 07:46:58

2.8k

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Proof of $\sup AB=\max\{\sup A\sup B,\sup A\inf B,\inf A\sup B,\inf A\inf B\}$

Published on 19 Aug 2016 - 7:46

score 310 · Answer 10 · 2016-08-19 23:38:09

310

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proving $\left|\overline\int_a^b f(x)\ dx\right|\le \overline{\int_a^b}|f(x)|\ dx$

Published on 19 Aug 2016 - 23:38

score 2.8k · Answer 11 · 2016-08-20 00:23:48

2.8k

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if $f$ is continuous, $f(x)\ge 0$ and $\int_a^bf(x)\ dx = 0$, then $f(x) = 0$

Published on 20 Aug 2016 - 0:23

score 200 · Answer 12 · 2016-08-23 01:15:21

200

Views

Comparing 2-norm of two vectors

Published on 23 Aug 2016 - 1:15

score 220 · Answer 13 · 2016-08-25 03:39:22

220

Views

If $0<a<$1, show that $\inf{a^n}=0$

Published on 25 Aug 2016 - 3:39

score 41 · Answer 14 · 2026-03-29 03:35:30

41

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Show that there exists a sequence $ (a_n)\subset T$ for which $|a_n-a| \lneq 1/3^n $ for all n

Published on 29 Mar 2026 - 3:35

score 564 · Answer 15 · 2016-08-30 16:07:33

564

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Proving that for a Dedekind cut $\alpha$ and positive rational $w$, $\exists{n\in\mathbb{Z}}$ such that $nw\in{\alpha}$ but $(n+1)w\notin{\alpha}$

Published on 30 Aug 2016 - 16:07

List Question

Is $\emptyset$ bounded? Why then $\inf \emptyset = \infty$ is reasonable?

Proof that $\lim\limits_{n\to\infty} \frac1{A_n}\sum_{k=1}^{n} { \mathbb{E} (a_k Y_k) } =0$.

how to determine the infimum of a multivariate function?

Supremum with respect to one variable is continuous (proof verification)

Proving $f(0) = 0, f(x) = \frac{1}{2^n}$ when $\frac{1}{2^{n+1}}<x<\frac{1}{2^n}$ is integrable

Domain monotonicity - $\mu_n (\Omega_2) \leq \mu_n (\Omega_1)$

Why must there exist a sequence $r_k ∈ R$ such that $r_k→r$?

Compute $\sup\limits_{x\in (0,2)}\left|\operatorname{cosh}\left(x^2-x-1\right)\right|$

Proof of $\sup AB=\max\{\sup A\sup B,\sup A\inf B,\inf A\sup B,\inf A\inf B\}$

proving $\left|\overline\int_a^b f(x)\ dx\right|\le \overline{\int_a^b}|f(x)|\ dx$

if $f$ is continuous, $f(x)\ge 0$ and $\int_a^bf(x)\ dx = 0$, then $f(x) = 0$

Comparing 2-norm of two vectors

If $0<a<$1, show that $\inf{a^n}=0$

Show that there exists a sequence $ (a_n)\subset T$ for which $|a_n-a| \lneq 1/3^n $ for all n

Proving that for a Dedekind cut $\alpha$ and positive rational $w$, $\exists{n\in\mathbb{Z}}$ such that $nw\in{\alpha}$ but $(n+1)w\notin{\alpha}$

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