Question

If $b > 1$ and $B(r)$ is the set of all numbers $b^t$, where $t$ is rational and $t \leq r$, prove that $b^r = \sup B(r)$ where $r$ is rational.

score 435 · Answer 1 · 2014-01-15 21:18:12

435

Views

If $b > 1$ and $B(r)$ is the set of all numbers $b^t$, where $t$ is rational and $t \leq r$, prove that $b^r = \sup B(r)$ where $r$ is rational.

Published on 15 Jan 2014 - 21:18

score 43 · Answer 2 · 2014-01-22 15:49:02

43

Views

an example of supremum using relation other than <. like using divides etc??

Published on 22 Jan 2014 - 15:49

score 1.4k · Answer 3 · 2014-02-01 12:23:36

1.4k

Views

Supremum calculation

Published on 01 Feb 2014 - 12:23

score 458 · Answer 4 · 2014-02-05 21:45:42

458

Views

Example of a set of real numbers $S$ where $\inf S = \sup S$?

Published on 05 Feb 2014 - 21:45

score 7k · Answer 5 · 2014-02-07 14:57:53

7k

Views

Show that: $\inf(A+B) = \inf(A)+ \inf(B)$

Published on 07 Feb 2014 - 14:57

score 466 · Answer 6 · 2014-02-08 15:46:22

466

Views

Determine whether the following subsets of $\mathbb{R}$ are bounded.

Published on 08 Feb 2014 - 15:46

score 7.5k · Answer 7 · 2014-02-08 16:45:33

7.5k

Views

Prove that infimum (A)=0 and that supremum (A)=1 in the following set

Published on 08 Feb 2014 - 16:45

score 399 · Answer 8 · 2014-02-10 23:39:22

399

Views

Are sup, inf, max, min correct for the set $\{\frac{x}{x+1}: x \in A\}$?

Published on 10 Feb 2014 - 23:39

score 77 · Answer 9 · 2014-02-14 10:08:50

77

Views

$\sup_{m \geq n} \, \operatorname{ess sup} |u_n - u_m| = \operatorname{ess sup} \, \sup_{m \geq n} |u_n - u_m|$

Published on 14 Feb 2014 - 10:08

score 2.5k · Answer 10 · 2026-02-23 16:43:01

2.5k

Views

Pointwise infimum of an arbitrary collection of upper semicontinuous functions is upper semicontinuous

Published on 23 Feb 2026 - 16:43

score 1.2k · Answer 11 · 2017-04-09 21:55:24

1.2k

Views

Convergence of GANs

Published on 09 Apr 2017 - 21:55

score 1.4k · Answer 12 · 2026-02-23 16:42:02

1.4k

Views

Prove by definition that every upper semi-continuous function can be expressed as infimum of a sequence of continuous functions.

Published on 23 Feb 2026 - 16:42

score 366 · Answer 13 · 2017-04-10 06:25:06

366

Views

Show that convergence and infimum-supremum are the same.

Published on 10 Apr 2017 - 6:25

score 549 · Answer 14 · 2017-04-10 19:44:33

549

Views

Proving the infimum of A:=(m,n) is m

Published on 10 Apr 2017 - 19:44

score 1.5k · Answer 15 · 2026-03-29 17:25:38

1.5k

Views

Prove an inequality involving infimum and supremum

Published on 29 Mar 2026 - 17:25

List Question

If $b > 1$ and $B(r)$ is the set of all numbers $b^t$, where $t$ is rational and $t \leq r$, prove that $b^r = \sup B(r)$ where $r$ is rational.

an example of supremum using relation other than <. like using divides etc??

Supremum calculation

Example of a set of real numbers $S$ where $\inf S = \sup S$?

Show that: $\inf(A+B) = \inf(A)+ \inf(B)$

Determine whether the following subsets of $\mathbb{R}$ are bounded.

Prove that infimum (A)=0 and that supremum (A)=1 in the following set

Are sup, inf, max, min correct for the set $\{\frac{x}{x+1}: x \in A\}$?

$\sup_{m \geq n} \, \operatorname{ess sup} |u_n - u_m| = \operatorname{ess sup} \, \sup_{m \geq n} |u_n - u_m|$

Pointwise infimum of an arbitrary collection of upper semicontinuous functions is upper semicontinuous

Convergence of GANs

Prove by definition that every upper semi-continuous function can be expressed as infimum of a sequence of continuous functions.

Show that convergence and infimum-supremum are the same.

Proving the infimum of A:=(m,n) is m

Prove an inequality involving infimum and supremum

Trending Questions

Popular # Hahtags

Popular Questions