Question

The infimum over all partitions is the same as the infimum over all partitions including a fixed partition $Q$

score 42 · Answer 1 · 2026-02-23 12:06:37

42

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The infimum over all partitions is the same as the infimum over all partitions including a fixed partition $Q$

Published on 23 Feb 2026 - 12:06

score 282 · Answer 2 · 2022-03-09 20:45:57

282

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Oscillation of the function at each point

Published on 09 Mar 2022 - 20:45

score 87 · Answer 3 · 2022-03-10 15:58:19

87

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If $a_0<\dots<a_n<b_n<\dots<b_0$ for any $n\in\Bbb N$ then $\sup( a_n)\le\inf(b_n)$?

Published on 10 Mar 2022 - 15:58

score 101 · Answer 4 · 2022-03-11 14:44:31

101

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How can you show this convergence for the supremum?

Published on 11 Mar 2022 - 14:44

score 43 · Answer 5 · 2022-03-12 17:10:28

43

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How do I prove that the following set is limited?

Published on 12 Mar 2022 - 17:10

score 153 · Answer 6 · 2022-03-13 19:05:58

153

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Exercise 4, Section 24 of Munkres’ Topology

Published on 13 Mar 2022 - 19:05

score 18 · Answer 7 · 2026-03-17 13:41:53

18

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$\underset{\omega}{\max}\; \omega^{\top}\cdot F(\omega') \leq \underset{\omega}{\max}\; \omega^{\top}\cdot F(\omega),\; \forall \omega'?$

Published on 17 Mar 2026 - 13:41

score 15 · Answer 8 · 2026-03-03 23:25:16

15

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Inequality searching for an upper-bound

Published on 03 Mar 2026 - 23:25

score 98 · Answer 9 · 2022-03-21 17:28:12

98

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Infimum of $\left\{\left|\sqrt{m} - \sqrt{n}\right|\;: \;m,n \in\mathbb{N},\; m≠n\right\}$

Published on 21 Mar 2022 - 17:28

score 32 · Answer 10 · 2026-02-23 11:59:35

32

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Useful properties for integration

Published on 23 Feb 2026 - 11:59

score 39 · Answer 11 · 2022-03-23 23:12:51

39

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Let B={$\frac{m^2-n}{m^2+n^2}: n,m \in \mathbb{N}, m>n$}. Prove $supA=1$ and $infA=\frac{1}{2}$

Published on 23 Mar 2022 - 23:12

score 264 · Answer 12 · 2022-03-25 22:03:27

264

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If a sequence of random variable is bounded in probability(Op(1)), then will its supremum be finite with probability 1(P (supn|Xn|<infinity)=1)?

Published on 25 Mar 2022 - 22:03

score 63 · Answer 13 · 2022-03-28 13:16:27

63

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Is it always true that the maximum of a closed bounded set, $[a,b]$, is also the supremum

Published on 28 Mar 2022 - 13:16

score 216 · Answer 14 · 2026-03-25 09:29:58

216

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How we can we prove that for any $b > a, x > 0$, $\frac{2}{\pi} (1-\frac{a}{b})<\sup|\frac{\sin(ax)}{ax} - \frac{\sin(bx)}{bx}|<4(1-\frac{a}{b})$

Published on 25 Mar 2026 - 9:29

score 62 · Answer 15 · 2022-03-31 16:48:00

62

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Upper bounds, infimum and supremum

Published on 31 Mar 2022 - 16:48

List Question

The infimum over all partitions is the same as the infimum over all partitions including a fixed partition $Q$

Oscillation of the function at each point

If $a_0<\dots<a_n<b_n<\dots<b_0$ for any $n\in\Bbb N$ then $\sup( a_n)\le\inf(b_n)$?

How can you show this convergence for the supremum?

How do I prove that the following set is limited?

Exercise 4, Section 24 of Munkres’ Topology

$\underset{\omega}{\max}\; \omega^{\top}\cdot F(\omega') \leq \underset{\omega}{\max}\; \omega^{\top}\cdot F(\omega),\; \forall \omega'?$

Inequality searching for an upper-bound

Infimum of $\left\{\left|\sqrt{m} - \sqrt{n}\right|\;: \;m,n \in\mathbb{N},\; m≠n\right\}$

Useful properties for integration

Let B={$\frac{m^2-n}{m^2+n^2}: n,m \in \mathbb{N}, m>n$}. Prove $supA=1$ and $infA=\frac{1}{2}$

If a sequence of random variable is bounded in probability(Op(1)), then will its supremum be finite with probability 1(P (supn|Xn|<infinity)=1)?

Is it always true that the maximum of a closed bounded set, $[a,b]$, is also the supremum

How we can we prove that for any $b > a, x > 0$, $\frac{2}{\pi} (1-\frac{a}{b})<\sup|\frac{\sin(ax)}{ax} - \frac{\sin(bx)}{bx}|<4(1-\frac{a}{b})$

Upper bounds, infimum and supremum

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