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The proof of existence of supremum for a non-empty set which has an upper bound

score 1.3k · Answer 1 · 2021-09-14 16:48:59

1.3k

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The proof of existence of supremum for a non-empty set which has an upper bound

Published on 14 Sep 2021 - 16:48

score 272 · Answer 2 · 2021-09-15 15:47:04

272

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Find the minimum value of: $\dfrac{a}{b+3a}+\dfrac{b}{c+3b}+\dfrac{c}{a+3c}$

Published on 15 Sep 2021 - 15:47

score 24 · Answer 3 · 2021-09-17 10:49:03

24

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If $0<\varphi_{n_k}\xrightarrow{k\to\infty}\varphi\ne0$ for some $(n_k)$, are we able to conclude $\inf_{n\in\mathbb N}\varphi_n(x)>0$ for all $x$?

Published on 17 Sep 2021 - 10:49

score 370 · Answer 4 · 2021-09-17 23:15:32

370

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Proving Riemann integrability for characteristic function of interval

Published on 17 Sep 2021 - 23:15

score 202 · Answer 5 · 2021-09-21 13:48:26

202

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Find the supremum of $A=\left\{\frac{n}{n+1}\right\} n \in \mathbb{N^*}$

Published on 21 Sep 2021 - 13:48

score 96 · Answer 6 · 2021-09-22 12:38:18

96

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What is the infimum of $\left\{\frac{1}{2^x},x\in\mathbb{N}\right\}$? Prove it.

Published on 22 Sep 2021 - 12:38

score 101 · Answer 7 · 2021-09-24 18:26:21

101

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$a^*$ and $a^{**}$ in wikipedia's proof of IVT

Published on 24 Sep 2021 - 18:26

score 493 · Answer 8 · 2021-09-25 02:28:30

493

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Proof of supremum of rationals less than $\sqrt 2$

Published on 25 Sep 2021 - 2:28

score 1.7k · Answer 9 · 2026-04-08 16:14:47

1.7k

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Continuous function on compact set attains its maximum and minimum.

Published on 08 Apr 2026 - 16:14

score 17 · Answer 10 · 2026-03-12 03:09:18

17

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Problem involving supremum inequality

Published on 12 Mar 2026 - 3:09

score 155 · Answer 11 · 2026-04-06 22:40:06

155

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Supremum property on ordered fields.

Published on 06 Apr 2026 - 22:40

score 100 · Answer 12 · 2021-09-29 12:06:12

100

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how show that $b$ is the supremum of an interval $[a,b)$

Published on 29 Sep 2021 - 12:06

score 116 · Answer 13 · 2026-03-18 02:19:33

116

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Intuition for the "Flip Flop Formula" for the generalized inverse of non-decreasing functions

Published on 18 Mar 2026 - 2:19

score 182 · Answer 14 · 2026-02-26 20:01:39

182

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$\liminf (f_n+g_n)=\liminf f_n + \liminf g_n$

Published on 26 Feb 2026 - 20:01

score 67 · Answer 15 · 2021-09-30 17:44:10

67

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Finding $\sup(a_n)$ and $\inf(a_n)$

Published on 30 Sep 2021 - 17:44

List Question

The proof of existence of supremum for a non-empty set which has an upper bound

Find the minimum value of: $\dfrac{a}{b+3a}+\dfrac{b}{c+3b}+\dfrac{c}{a+3c}$

If $0<\varphi_{n_k}\xrightarrow{k\to\infty}\varphi\ne0$ for some $(n_k)$, are we able to conclude $\inf_{n\in\mathbb N}\varphi_n(x)>0$ for all $x$?

Proving Riemann integrability for characteristic function of interval

Find the supremum of $A=\left\{\frac{n}{n+1}\right\} n \in \mathbb{N^*}$

What is the infimum of $\left\{\frac{1}{2^x},x\in\mathbb{N}\right\}$? Prove it.

$a^*$ and $a^{**}$ in wikipedia's proof of IVT

Proof of supremum of rationals less than $\sqrt 2$

Continuous function on compact set attains its maximum and minimum.

Problem involving supremum inequality

Supremum property on ordered fields.

how show that $b$ is the supremum of an interval $[a,b)$

Intuition for the "Flip Flop Formula" for the generalized inverse of non-decreasing functions

$\liminf (f_n+g_n)=\liminf f_n + \liminf g_n$

Finding $\sup(a_n)$ and $\inf(a_n)$

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