Question

Sum of infimums

score 375 · Answer 1 · 2022-09-15 13:55:13

375

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Sum of infimums

Published on 15 Sep 2022 - 13:55

score 58 · Answer 2 · 2022-09-16 13:57:02

58

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Proof help: $\inf_m a_m + \inf_n b_n \leq \inf_n (a_n+b_n)$ and $\inf_m a_m + \inf_n b_n = \inf _{m,n} a_m + b_n$

Published on 16 Sep 2022 - 13:57

score 337 · Answer 3 · 2022-09-18 16:41:07

337

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Certain step that $\{x\in \mathbb{Q}\mid x^2<2\}$ has no supremum in $\mathbb{Q}$

Published on 18 Sep 2022 - 16:41

score 53 · Answer 4 · 2022-09-18 20:42:17

53

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Supremum of $\cos(n)/n$ for $n\geq 1$

Published on 18 Sep 2022 - 20:42

score 122 · Answer 5 · 2026-04-10 17:07:09

122

Views

Can an infinite increasing sequence contain its supremum

Published on 10 Apr 2026 - 17:07

score 84 · Answer 6 · 2022-09-19 11:47:04

84

Views

Supremum and Infimum for sequence that is not monotone increasing or decreasing.

Published on 19 Sep 2022 - 11:47

score 46 · Answer 7 · 2026-04-08 21:57:06

46

Views

Confusion about definition of least upper bound

Published on 08 Apr 2026 - 21:57

score 49 · Answer 8 · 2026-04-08 09:36:25

49

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Let $B \subset \mathbb{R}$ be a non-empty subset. Let $d = inf B$. For every $\epsilon > 0$, the set $[d, d + \epsilon) \cap B$ is non-empty.

Published on 08 Apr 2026 - 9:36

score 98 · Answer 9 · 2022-09-22 13:37:15

98

Views

Shorter way to prove $|\underset{x \in A}{\text{inf}}f(x)-\underset{x \in A}{\text{inf}}g(x)|\leq \underset{x \in A}{\text{sup}} |f(x)-g(x)|$

Published on 22 Sep 2022 - 13:37

score 38 · Answer 10 · 2022-09-25 14:42:23

38

Views

How can I prove that $\sup\{\Phi(f):f\in \bar B\}=1$ if $\bar B=\{f\in C\left([0,1]\right): d(f,0)\leq 1\}$?

Published on 25 Sep 2022 - 14:42

score 524 · Answer 11 · 2026-04-11 12:54:53

524

Views

Is the minization of a strictly convex function still strictly convex?

Published on 11 Apr 2026 - 12:54

score 41 · Answer 12 · 2026-04-10 02:26:08

41

Views

Is this property about a monotonic function between DCPOs true?

Published on 10 Apr 2026 - 2:26

score 129 · Answer 13 · 2026-04-10 03:38:21

129

Views

Proof of contradiction when showing the supremum of a function

Published on 10 Apr 2026 - 3:38

score 260 · Answer 14 · 2022-10-03 04:12:24

260

Views

Comparison Property of Supremum Proof

Published on 03 Oct 2022 - 4:12

score 65 · Answer 15 · 2026-03-29 16:02:52

65

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Infimums of subsets of monoid.

Published on 29 Mar 2026 - 16:02

List Question

Sum of infimums

Proof help: $\inf_m a_m + \inf_n b_n \leq \inf_n (a_n+b_n)$ and $\inf_m a_m + \inf_n b_n = \inf _{m,n} a_m + b_n$

Certain step that $\{x\in \mathbb{Q}\mid x^2<2\}$ has no supremum in $\mathbb{Q}$

Supremum of $\cos(n)/n$ for $n\geq 1$

Can an infinite increasing sequence contain its supremum

Supremum and Infimum for sequence that is not monotone increasing or decreasing.

Confusion about definition of least upper bound

Let $B \subset \mathbb{R}$ be a non-empty subset. Let $d = inf B$. For every $\epsilon > 0$, the set $[d, d + \epsilon) \cap B$ is non-empty.

Shorter way to prove $|\underset{x \in A}{\text{inf}}f(x)-\underset{x \in A}{\text{inf}}g(x)|\leq \underset{x \in A}{\text{sup}} |f(x)-g(x)|$

How can I prove that $\sup\{\Phi(f):f\in \bar B\}=1$ if $\bar B=\{f\in C\left([0,1]\right): d(f,0)\leq 1\}$?

Is the minization of a strictly convex function still strictly convex?

Is this property about a monotonic function between DCPOs true?

Proof of contradiction when showing the supremum of a function

Comparison Property of Supremum Proof

Infimums of subsets of monoid.

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