Question

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

score 378 · Answer 1 · 2026-03-26 12:37:29

378

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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 352 · Answer 2 · 2020-03-25 17:45:44

352

Views

Proving that $\lim_{x \to x_0} \cos(x) = \cos(x_0)$

Published on 25 Mar 2020 - 17:45

score 134 · Answer 3 · 2020-03-25 18:05:32

134

Views

Proving that $\lim_{x \to 0} \frac{\sin(x)}{x} = 1$

Published on 25 Mar 2020 - 18:05

score 1.8k · Answer 4 · 2020-03-25 20:17:04

1.8k

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Proof that if the limit exists, then the function is bounded in some neighbourhood

Published on 25 Mar 2020 - 20:17

score 167 · Answer 5 · 2026-03-26 22:53:36

167

Views

Is $\sin(\alpha)=\frac{\tan(\alpha)}{\sqrt{1+\tan^2(\alpha)}}$ a true statment?

Published on 26 Mar 2026 - 22:53

score 342 · Answer 6 · 2026-03-27 01:43:24

342

Views

Examples of compact operators, solution verification

Published on 27 Mar 2026 - 1:43

score 111 · Answer 7 · 2026-03-28 04:34:12

111

Views

Rohlin lemma for aperiodic atomless invertible measure preserving systems

Published on 28 Mar 2026 - 4:34

score 20 · Answer 8 · 2020-03-25 23:51:21

20

Views

Proof of a Logical Statement.

Published on 25 Mar 2020 - 23:51

score 123 · Answer 9 · 2026-03-27 01:42:11

123

Views

if $\Lambda = \Lambda ^2$ be a compact operator on a banach space , then $Range(\Lambda)$ is finite dimensional

Published on 27 Mar 2026 - 1:42

score 170 · Answer 10 · 2026-03-31 11:25:11

170

Views

Doubt about the logic defining transitivity of a relation

Published on 31 Mar 2026 - 11:25

score 213 · Answer 11 · 2020-03-26 06:12:02

213

Views

Prove that $\lim_{x \to 0} \frac{1}{x}$ does not exist

Published on 26 Mar 2020 - 6:12

score 32 · Answer 12 · 2020-03-26 08:16:45

32

Views

Prove that if $f$ has a nonzero limit at $x_0$, then there is a deleted neighbourhood where it has the same sign as the limit.

Published on 26 Mar 2020 - 8:16

score 37 · Answer 13 · 2020-03-26 09:13:24

37

Views

Prove that $f(x) \to c$ as $x \to x_0$ iff $f(x) = c+\alpha(x)$, where $\alpha(x) \to 0$ as $x \to x_0$

Published on 26 Mar 2020 - 9:13

score 110 · Answer 14 · 2026-03-27 00:57:12

110

Views

Why is $\mathcal{P}(A\cup B) \not\subset \mathcal{P}(A)\cup\mathcal{P}(B)$?

Published on 27 Mar 2026 - 0:57

score 71 · Answer 15 · 2026-03-26 04:38:03

71

Views

The axiom quotient and any property of a group.

Published on 26 Mar 2026 - 4:38

List Question

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

Proving that $\lim_{x \to x_0} \cos(x) = \cos(x_0)$

Proving that $\lim_{x \to 0} \frac{\sin(x)}{x} = 1$

Proof that if the limit exists, then the function is bounded in some neighbourhood

Is $\sin(\alpha)=\frac{\tan(\alpha)}{\sqrt{1+\tan^2(\alpha)}}$ a true statment?

Examples of compact operators, solution verification

Rohlin lemma for aperiodic atomless invertible measure preserving systems

Proof of a Logical Statement.

if $\Lambda = \Lambda ^2$ be a compact operator on a banach space , then $Range(\Lambda)$ is finite dimensional

Doubt about the logic defining transitivity of a relation

Prove that $\lim_{x \to 0} \frac{1}{x}$ does not exist

Prove that if $f$ has a nonzero limit at $x_0$, then there is a deleted neighbourhood where it has the same sign as the limit.

Prove that $f(x) \to c$ as $x \to x_0$ iff $f(x) = c+\alpha(x)$, where $\alpha(x) \to 0$ as $x \to x_0$

Why is $\mathcal{P}(A\cup B) \not\subset \mathcal{P}(A)\cup\mathcal{P}(B)$?

The axiom quotient and any property of a group.

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