Question

Prove the following result: if $f(x) \geq g(x)$ for all $x\in I$, then $p.c.\int_{I}f \geq p.c.\int_{I}g$.

score 64 · Answer 1 · 2026-04-09 12:03:49

64

Views

Prove the following result: if $f(x) \geq g(x)$ for all $x\in I$, then $p.c.\int_{I}f \geq p.c.\int_{I}g$.

Published on 09 Apr 2026 - 12:03

score 185 · Answer 2 · 2026-04-14 21:56:39

185

Views

Prove that the set of rapidly increasing functions is uncountable using diagonalization

Published on 14 Apr 2026 - 21:56

score 1k · Answer 3 · 2026-03-26 02:55:58

1k

Views

$G$ is solvable implies there exists a chain of normal subgroups such that adjacent quotients are cyclic

Published on 26 Mar 2026 - 2:55

score 469 · Answer 4 · 2026-04-15 21:27:47

469

Views

Let $X$ be a subset of the real line. Then prove that $X$ is bounded and connected if and only if $X$ is a bounded interval.

Published on 15 Apr 2026 - 21:27

score 228 · Answer 5 · 2026-04-09 12:03:38

228

Views

Prove that if the partition $\textbf{P}'$ is finer than $\textbf{P}$, then $f$ keeps piecewise constant

Published on 09 Apr 2026 - 12:03

score 63 · Answer 6 · 2026-04-17 13:54:21

63

Views

Find infimum of the sets of number $x + \frac{1}{x} $

Published on 17 Apr 2026 - 13:54

score 101 · Answer 7 · 2026-04-13 10:02:50

101

Views

Limit of expected value of supremum and infimum

Published on 13 Apr 2026 - 10:02

score 276 · Answer 8 · 2026-04-14 11:03:16

276

Views

Proving the generalized associativity for groups

Published on 14 Apr 2026 - 11:03

score 692 · Answer 9 · 2026-04-17 17:38:40

692

Views

Let $L$ be the distance between two parallel normals of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, $a>b$, then find maximum value of $L$

Published on 17 Apr 2026 - 17:38

score 129 · Answer 10 · 2026-04-13 09:32:47

129

Views

Analytic function on the complex plane except the negative real axis

Published on 13 Apr 2026 - 9:32

score 120 · Answer 11 · 2026-04-13 12:36:10

120

Views

Show that, the spiral and the half straight line in $\Bbb{R}^2$ are homeomorphic.

Published on 13 Apr 2026 - 12:36

score 80 · Answer 12 · 2026-04-14 09:47:36

80

Views

Rudin POMA Chapter 1 exercise 18

Published on 14 Apr 2026 - 9:47

score 44 · Answer 13 · 2026-04-12 10:13:57

44

Views

Decide if a function is Riemann Integrable

Published on 12 Apr 2026 - 10:13

score 307 · Answer 14 · 2026-04-09 18:54:47

307

Views

Proof of the Density of Irrationals

Published on 09 Apr 2026 - 18:54

score 72 · Answer 15 · 2026-04-14 13:33:35

72

Views

Explain a section of Euclid's Theorem on an infinite number of prime numbers.

Published on 14 Apr 2026 - 13:33

List Question

Prove the following result: if $f(x) \geq g(x)$ for all $x\in I$, then $p.c.\int_{I}f \geq p.c.\int_{I}g$.

Prove that the set of rapidly increasing functions is uncountable using diagonalization

$G$ is solvable implies there exists a chain of normal subgroups such that adjacent quotients are cyclic

Let $X$ be a subset of the real line. Then prove that $X$ is bounded and connected if and only if $X$ is a bounded interval.

Prove that if the partition $\textbf{P}'$ is finer than $\textbf{P}$, then $f$ keeps piecewise constant

Find infimum of the sets of number $x + \frac{1}{x} $

Limit of expected value of supremum and infimum

Proving the generalized associativity for groups

Let $L$ be the distance between two parallel normals of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, $a>b$, then find maximum value of $L$

Analytic function on the complex plane except the negative real axis

Show that, the spiral and the half straight line in $\Bbb{R}^2$ are homeomorphic.

Rudin POMA Chapter 1 exercise 18

Decide if a function is Riemann Integrable

Proof of the Density of Irrationals

Explain a section of Euclid's Theorem on an infinite number of prime numbers.

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