List questions from proof-verification

Published on 11 Apr 2026 - 16:41

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Let $F$ be a field. How do we show that maximal ideals of $F[x]$ are the principal ideals generated by the monic irreducible polynomials?

Published on 14 Apr 2026 - 12:27

70

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A power series which is one to one

Published on 10 Apr 2026 - 3:34

218

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Given the joint probability density function of the random variables $X$ and $Y$, determine $\textbf{P}(X < Y)$

Published on 14 Apr 2026 - 18:19

111

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If $G$ is a group and $g\in G$, then for all $n,m\in\mathbb{Z}$, we have the following properties.

Published on 14 Apr 2026 - 20:59

49

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Verification of a vector space

Published on 12 Apr 2026 - 20:08

75

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Counting a Directional derivative.

Published on 11 Apr 2026 - 10:02

56

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Show that $G'$ contains a subgroup of order $d$

Published on 15 Apr 2026 - 16:59

116

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A question about the Vitali set.

Published on 10 Apr 2026 - 18:13

20

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sum of Time complexities

Published on 17 Apr 2026 - 5:43

64

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Prove: [0,1] is supercompact

Published on 10 Apr 2026 - 17:38

67

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Transformation of random variables: what went wrong?

Published on 10 Apr 2026 - 15:02

230

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without computing it, show that $I = \mathbb{E}[e^{XY} |X] \geq 1$

Published on 15 Apr 2026 - 19:22

66

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the truth of $\bigcap_n L^1(\mu_n)=L^1(\mu)$ where the measures $\mu_n$ converge to $\mu$

Published on 16 Apr 2026 - 16:02

63

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$\lim_{n\to +\infty} |(2n\pi+1/n) \sin(2n\pi+1/n)|$, $n\in \mathbb N$

Published on 17 Apr 2026 - 5:11

List Question

Naive question about continuous random variable: solution verification

Let $F$ be a field. How do we show that maximal ideals of $F[x]$ are the principal ideals generated by the monic irreducible polynomials?

A power series which is one to one

Given the joint probability density function of the random variables $X$ and $Y$, determine $\textbf{P}(X < Y)$

If $G$ is a group and $g\in G$, then for all $n,m\in\mathbb{Z}$, we have the following properties.

Verification of a vector space

Counting a Directional derivative.

Show that $G'$ contains a subgroup of order $d$

A question about the Vitali set.

sum of Time complexities

Prove: [0,1] is supercompact

Transformation of random variables: what went wrong?

without computing it, show that $I = \mathbb{E}[e^{XY} |X] \geq 1$

the truth of $\bigcap_n L^1(\mu_n)=L^1(\mu)$ where the measures $\mu_n$ converge to $\mu$

$\lim_{n\to +\infty} |(2n\pi+1/n) \sin(2n\pi+1/n)|$, $n\in \mathbb N$

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