Question

Proving set has infimum and unbounded above

score 180 · Answer 1 · 2020-03-24 14:26:42

180

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Proving set has infimum and unbounded above

Published on 24 Mar 2020 - 14:26

score 45 · Answer 2 · 2020-03-25 15:24:15

45

Views

Prove that the sequence $(f_n)_{n \geq 1}$ does not have a convergent subsequence

Published on 25 Mar 2020 - 15:24

score 378 · Answer 3 · 2026-03-26 12:37:29

378

Views

Bounded variation implies supremum over all partitions is finite. What if we impose that the bound depends on the partition?

Published on 26 Mar 2026 - 12:37

score 161 · Answer 4 · 2026-03-28 02:44:52

161

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Let A = {z ∈ R : there exists n, m ∈ N such that z = 1/n − 1/m }. Prove, using definition(s) and/or result(s) from the lectures, that sup(A) = 1

Published on 28 Mar 2026 - 2:44

score 79 · Answer 5 · 2026-03-28 07:43:03

79

Views

Find limsup and liminf of a sequence

Published on 28 Mar 2026 - 7:43

score 65 · Answer 6 · 2020-03-27 01:57:41

65

Views

Need help on answering proof question on polynomials p1,p2 of degree

Published on 27 Mar 2020 - 1:57

score 50 · Answer 7 · 2020-03-27 09:10:12

50

Views

Show that if a subset $S$ of $R$ has a maximum element $y$ (in other words, $y \in S$ and $x \leq y$ for all $x \in S$), then $y =\sup S$.

Published on 27 Mar 2020 - 9:10

score 55 · Answer 8 · 2020-03-27 12:50:19

55

Views

Measurable functions(probability course)- proving a limit superior inequality for a sequence of functions

Published on 27 Mar 2020 - 12:50

score 170 · Answer 9 · 2026-03-17 23:00:50

170

Views

Is the generalized inverse of the gen. inverse of $f$ equal to $f$?

Published on 17 Mar 2026 - 23:00

score 118 · Answer 10 · 2020-03-29 09:37:07

118

Views

Suppose that S is a non-empty subset of $R$. Prove that is $M=supS$, then for every $\epsilon > 0$ there exists $s \in S$ such that $s>M - \epsilon$

Published on 29 Mar 2020 - 9:37

score 229 · Answer 11 · 2026-03-28 18:14:17

229

Views

Understanding Wiki proof - Least upper bound property

Published on 28 Mar 2026 - 18:14

score 631 · Answer 12 · 2020-03-30 04:21:03

631

Views

What's wrong with my proof of $\inf S = -\sup(-S)$?

Published on 30 Mar 2020 - 4:21

score 336 · Answer 13 · 2020-03-30 09:46:20

336

Views

Let $S$ and $T$ be non-empty bounded sets of real numbers and suppose that $s<t$ for every $s \in S$ and every $t \in.T$.

Published on 30 Mar 2020 - 9:46

score 222 · Answer 14 · 2026-03-25 18:31:22

222

Views

Examining the theorem, for all $\epsilon \gt 0$, if $x \le y + \epsilon$, then $x \le y$

Published on 25 Mar 2026 - 18:31

score 789 · Answer 15 · 2020-04-04 14:00:25

789

Views

Confusion about whether a supremum of a set can be a limit point if it belongs to the set.

Published on 04 Apr 2020 - 14:00

List Question

Proving set has infimum and unbounded above

Prove that the sequence $(f_n)_{n \geq 1}$ does not have a convergent subsequence

Bounded variation implies supremum over all partitions is finite. What if we impose that the bound depends on the partition?

Let A = {z ∈ R : there exists n, m ∈ N such that z = 1/n − 1/m }. Prove, using definition(s) and/or result(s) from the lectures, that sup(A) = 1

Find limsup and liminf of a sequence

Need help on answering proof question on polynomials p1,p2 of degree

Show that if a subset $S$ of $R$ has a maximum element $y$ (in other words, $y \in S$ and $x \leq y$ for all $x \in S$), then $y =\sup S$.

Measurable functions(probability course)- proving a limit superior inequality for a sequence of functions

Is the generalized inverse of the gen. inverse of $f$ equal to $f$?

Suppose that S is a non-empty subset of $R$. Prove that is $M=supS$, then for every $\epsilon > 0$ there exists $s \in S$ such that $s>M - \epsilon$

Understanding Wiki proof - Least upper bound property

What's wrong with my proof of $\inf S = -\sup(-S)$?

Let $S$ and $T$ be non-empty bounded sets of real numbers and suppose that $s<t$ for every $s \in S$ and every $t \in.T$.

Examining the theorem, for all $\epsilon \gt 0$, if $x \le y + \epsilon$, then $x \le y$

Confusion about whether a supremum of a set can be a limit point if it belongs to the set.

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