Question

Find and rigorously prove the supremum of the set:

score 61 · Answer 1 · 2021-04-06 00:13:02

61

Views

Find and rigorously prove the supremum of the set:

Published on 06 Apr 2021 - 0:13

score 28 · Answer 2 · 2021-04-06 16:03:15

28

Views

Show that $\inf_n\tau_n<t$ if and only if $\exists n:\tau_n<t$

Published on 06 Apr 2021 - 16:03

score 258 · Answer 3 · 2021-04-07 08:29:09

258

Views

Prove that $\sup\left (\frac{1}{A}\right )=\frac{1}{\inf A}.$

Published on 07 Apr 2021 - 8:29

score 288 · Answer 4 · 2021-04-07 15:25:48

288

Views

Supremum over real interval equals supremum over rational 'interval' for continuos functions?

Published on 07 Apr 2021 - 15:25

score 124 · Answer 5 · 2026-03-29 09:08:35

124

Views

Supremum and Continuity for function

Published on 29 Mar 2026 - 9:08

score 138 · Answer 6 · 2021-04-07 21:41:38

138

Views

What does it mean for a family of functions $\{f_n\}$ to be bounded?

Published on 07 Apr 2021 - 21:41

score 56 · Answer 7 · 2021-04-08 00:08:24

56

Views

Show that $\sup\ A < \sup\ B \implies \exists b\in B \ |\ b \ \text{is upper bound for} A$

Published on 08 Apr 2021 - 0:08

score 313 · Answer 8 · 2026-04-06 13:11:14

313

Views

Proving a certain inequality of infimums of upper Riemann integral

Published on 06 Apr 2026 - 13:11

score 376 · Answer 9 · 2026-03-30 09:51:39

376

Views

Prove: $\overline{\int_{a}^{b}} (g+f)(x) \ dx = \int\limits_a^b {{f(x)}dx}+ \overline{\int_{a}^{b}} g(x) \ dx$

Published on 30 Mar 2026 - 9:51

score 165 · Answer 10 · 2021-04-11 16:28:22

165

Views

Supremum of a sequence of real numbers

Published on 11 Apr 2021 - 16:28

score 793 · Answer 11 · 2021-04-12 00:02:35

793

Views

Let $K$ be a nonempty closed, convex subset of $R^d$. Prove that if $x\notin K$, then there exists a unique point $y\in K$ that is closest to $x$.

Published on 12 Apr 2021 - 0:02

score 62 · Answer 12 · 2021-04-12 12:52:34

62

Views

$f(x)=\sup\{|f_n(x)| \ :\ n=1,2,..\}<\infty$ find an example of the sequence $\{f_n\}$ such that, $\sup\{f(x)\ :\ 0<x<1\ \}=\infty$

Published on 12 Apr 2021 - 12:52

score 162 · Answer 13 · 2026-04-06 13:10:40

162

Views

Riemann integral $\underline{\int_a^b} \alpha f = \alpha \underline{\int_a^b} f$

Published on 06 Apr 2026 - 13:10

score 33 · Answer 14 · 2026-04-06 19:36:54

33

Views

S is a set of adherent values of a sequence $x_n$

Published on 06 Apr 2026 - 19:36

score 82 · Answer 15 · 2021-04-16 15:32:50

82

Views

Find $x$ such that $(ax)^{bx}>c$, where $a,b,c,x>0$

Published on 16 Apr 2021 - 15:32

List Question

Find and rigorously prove the supremum of the set:

Show that $\inf_n\tau_n<t$ if and only if $\exists n:\tau_n<t$

Prove that $\sup\left (\frac{1}{A}\right )=\frac{1}{\inf A}.$

Supremum over real interval equals supremum over rational 'interval' for continuos functions?

Supremum and Continuity for function

What does it mean for a family of functions $\{f_n\}$ to be bounded?

Show that $\sup\ A < \sup\ B \implies \exists b\in B \ |\ b \ \text{is upper bound for} A$

Proving a certain inequality of infimums of upper Riemann integral

Prove: $\overline{\int_{a}^{b}} (g+f)(x) \ dx = \int\limits_a^b {{f(x)}dx}+ \overline{\int_{a}^{b}} g(x) \ dx$

Supremum of a sequence of real numbers

Let $K$ be a nonempty closed, convex subset of $R^d$. Prove that if $x\notin K$, then there exists a unique point $y\in K$ that is closest to $x$.

$f(x)=\sup\{|f_n(x)| \ :\ n=1,2,..\}<\infty$ find an example of the sequence $\{f_n\}$ such that, $\sup\{f(x)\ :\ 0<x<1\ \}=\infty$

Riemann integral $\underline{\int_a^b} \alpha f = \alpha \underline{\int_a^b} f$

S is a set of adherent values of a sequence $x_n$

Find $x$ such that $(ax)^{bx}>c$, where $a,b,c,x>0$

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