Question

Max dimension of subspace $U\subseteq V$, where $V$ is a vector space of functions $[0,1]\rightarrow \Bbb R$

score 410 · Answer 1 · 2026-04-14 10:18:32

410

Views

Max dimension of subspace $U\subseteq V$, where $V$ is a vector space of functions $[0,1]\rightarrow \Bbb R$

Published on 14 Apr 2026 - 10:18

score 49 · Answer 2 · 2026-04-11 06:19:04

49

Views

quotient of monotonic transformation of a function

Published on 11 Apr 2026 - 6:19

score 70 · Answer 3 · 2026-04-15 13:42:46

70

Views

Is a function $f$ monotone decreasing if $\lim _{x\to b }f\left(x\right)\:=\:0$ and $f\left(x\right) \ge 0$ $\forall x \in [a,b]$?

Published on 15 Apr 2026 - 13:42

score 200 · Answer 4 · 2026-04-17 10:04:12

200

Views

$\frac{x^5}{5!}- \frac{x^7}{7!}+ \frac{x^9}{9!}+\dots>0$ holds for $x>0$

Published on 17 Apr 2026 - 10:04

score 85 · Answer 5 · 2026-04-11 23:26:15

85

Views

Show that $\operatorname{Im} f$ is a union of two disjoint intervals

Published on 11 Apr 2026 - 23:26

score 97 · Answer 6 · 2026-04-10 02:02:08

97

Views

Bounded completely monotone function has bounded derivative

Published on 10 Apr 2026 - 2:02

score 67 · Answer 7 · 2026-04-12 19:11:26

67

Views

An example for a function that is defined in $[0,1]\rightarrow \mathbb{R}$ and is integrable but is not monotone and not continuous in $[0,1]$

Published on 12 Apr 2026 - 19:11

score 105 · Answer 8 · 2026-05-10 15:52:11

105

Views

Nontrivial solutions to $\sum f(x) - \int f(x) = \gamma $?

Published on 10 May 2026 - 15:52

score 33 · Answer 9 · 2026-04-17 08:57:23

33

Views

Order in which to take max and square

Published on 17 Apr 2026 - 8:57

score 324 · Answer 10 · 2026-05-10 18:09:11

324

Views

Monotonicity of vector fields

Published on 10 May 2026 - 18:09

score 68 · Answer 11 · 2026-04-08 00:37:27

68

Views

Understanding proof of monotonic increasing function and continuity

Published on 08 Apr 2026 - 0:37

score 172 · Answer 12 · 2026-04-14 01:09:10

172

Views

Sufficient condition to show that f(x) is monotonic in some neighbourhood of x

Published on 14 Apr 2026 - 1:09

score 68 · Answer 13 · 2026-04-15 18:50:42

68

Views

If $g(.)$ is a monotonically increasing function and $a <b$, is $a<g(a)<g(b)<b$?

Published on 15 Apr 2026 - 18:50

score 733 · Answer 14 · 2026-04-14 11:27:33

733

Views

Maximum preserved under monotonic mapping

Published on 14 Apr 2026 - 11:27

score 423 · Answer 15 · 2026-04-16 09:53:59

423

Views

If $g:[0,1] \to \Bbb{R}$ such that $g(x)=g(y) \implies g'(x)=g'(y)$ for all $x,y \in (0,1)$, then $g$ is monotonic?

Published on 16 Apr 2026 - 9:53

List Question

Max dimension of subspace $U\subseteq V$, where $V$ is a vector space of functions $[0,1]\rightarrow \Bbb R$

quotient of monotonic transformation of a function

Is a function $f$ monotone decreasing if $\lim _{x\to b }f\left(x\right)\:=\:0$ and $f\left(x\right) \ge 0$ $\forall x \in [a,b]$?

$\frac{x^5}{5!}- \frac{x^7}{7!}+ \frac{x^9}{9!}+\dots>0$ holds for $x>0$

Show that $\operatorname{Im} f$ is a union of two disjoint intervals

Bounded completely monotone function has bounded derivative

An example for a function that is defined in $[0,1]\rightarrow \mathbb{R}$ and is integrable but is not monotone and not continuous in $[0,1]$

Nontrivial solutions to $\sum f(x) - \int f(x) = \gamma $?

Order in which to take max and square

Monotonicity of vector fields

Understanding proof of monotonic increasing function and continuity

Sufficient condition to show that f(x) is monotonic in some neighbourhood of x

If $g(.)$ is a monotonically increasing function and $a <b$, is $a<g(a)<g(b)<b$?

Maximum preserved under monotonic mapping

If $g:[0,1] \to \Bbb{R}$ such that $g(x)=g(y) \implies g'(x)=g'(y)$ for all $x,y \in (0,1)$, then $g$ is monotonic?

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