Question

If $0 \in P$ and $\sup\{x \in [0,1] : [0,x] \subseteq P\} = 1$, then $[0,1] \subseteq P$? (What if adding 3rd assumption?)

score 58 · Answer 1 · 2015-10-18 21:45:31

58

Views

If $0 \in P$ and $\sup\{x \in [0,1] : [0,x] \subseteq P\} = 1$, then $[0,1] \subseteq P$? (What if adding 3rd assumption?)

Published on 18 Oct 2015 - 21:45

score 719 · Answer 2 · 2015-10-19 15:10:39

719

Views

Definition of essential maximum and essential supremum

Published on 19 Oct 2015 - 15:10

score 295 · Answer 3 · 2015-10-19 16:40:08

295

Views

Finding and proving supremum and infimum

Published on 19 Oct 2015 - 16:40

score 1.3k · Answer 4 · 2026-04-02 19:12:26

1.3k

Views

If liminf exists, is the sequence is bounded below?

Published on 02 Apr 2026 - 19:12

score 66 · Answer 5 · 2015-10-21 04:37:46

66

Views

Given $S= \bigcap^{\infty}_{k=1}\left(1-\frac{1}{k}, 1+\frac{1}{k}\right)$, what is $\sup(S)$ and $\max(S)$?

Published on 21 Oct 2015 - 4:37

score 45 · Answer 6 · 2015-10-21 12:38:09

45

Views

Two nonempty sets that are bounded from above.

Published on 21 Oct 2015 - 12:38

score 311 · Answer 7 · 2015-10-21 16:36:25

311

Views

Understand a property of supremum and infinum

Published on 21 Oct 2015 - 16:36

score 645 · Answer 8 · 2015-10-21 17:36:23

645

Views

Let $A = \{\frac{m}{n}; m,n \in \mathbb{N} \ \text{and} \ m <2n\}$. Show that $\sup A = 2$.

Published on 21 Oct 2015 - 17:36

score 99 · Answer 9 · 2015-10-21 17:55:56

99

Views

Prove that $f(x) = d(x,X)$ is continuous on $M$.

Published on 21 Oct 2015 - 17:55

score 3.3k · Answer 10 · 2015-10-21 18:22:19

3.3k

Views

Prove that sup(A−B) = supA−inf B

Published on 21 Oct 2015 - 18:22

score 1.3k · Answer 11 · 2015-10-21 23:22:54

1.3k

Views

Infimum of this set (infinite intersection of intervals)

Published on 21 Oct 2015 - 23:22

score 286 · Answer 12 · 2015-10-23 11:45:32

286

Views

Can you use limits to calculate the supremum/infimum of a set?

Published on 23 Oct 2015 - 11:45

score 266 · Answer 13 · 2015-10-23 20:23:54

266

Views

Definition for supremum

Published on 23 Oct 2015 - 20:23

score 105 · Answer 14 · 2015-10-25 12:06:36

105

Views

Proof: Supremum of $\{\frac{x}{1+x}: x \in \mathbb{R}, x>0\}$ is 1

Published on 25 Oct 2015 - 12:06

score 326 · Answer 15 · 2015-10-26 03:49:32

326

Views

Help with a supremum Norm proof

Published on 26 Oct 2015 - 3:49

List Question

If $0 \in P$ and $\sup\{x \in [0,1] : [0,x] \subseteq P\} = 1$, then $[0,1] \subseteq P$? (What if adding 3rd assumption?)

Definition of essential maximum and essential supremum

Finding and proving supremum and infimum

If liminf exists, is the sequence is bounded below?

Given $S= \bigcap^{\infty}_{k=1}\left(1-\frac{1}{k}, 1+\frac{1}{k}\right)$, what is $\sup(S)$ and $\max(S)$?

Two nonempty sets that are bounded from above.

Understand a property of supremum and infinum

Let $A = \{\frac{m}{n}; m,n \in \mathbb{N} \ \text{and} \ m <2n\}$. Show that $\sup A = 2$.

Prove that $f(x) = d(x,X)$ is continuous on $M$.

Prove that sup(A−B) = supA−inf B

Infimum of this set (infinite intersection of intervals)

Can you use limits to calculate the supremum/infimum of a set?

Definition for supremum

Proof: Supremum of $\{\frac{x}{1+x}: x \in \mathbb{R}, x>0\}$ is 1

Help with a supremum Norm proof

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