Question

Is there a mistake in this proof of Hall's theorem?

score 591 · Answer 1 · 2026-04-11 18:06:26

591

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Is there a mistake in this proof of Hall's theorem?

Published on 11 Apr 2026 - 18:06

score 15.5k · Answer 2 · 2026-04-11 14:07:11

15.5k

Views

Transformation of a linear independent set is linearly independent

Published on 11 Apr 2026 - 14:07

score 195 · Answer 3 · 2026-04-16 11:19:05

195

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Let $(G, \cdot)$ be a group with the property that there exists $a \in G$ such that $x^3 = xax$, $\forall x \in G$. Prove $G$ is abelian.

Published on 16 Apr 2026 - 11:19

score 343 · Answer 4 · 2026-04-08 21:45:36

343

Views

Applying Cauchy's integral formula

Published on 08 Apr 2026 - 21:45

score 1.9k · Answer 5 · 2026-04-14 23:43:13

1.9k

Views

Homeomorphism $f : (–1,1) \rightarrow \mathbb{R}$

Published on 14 Apr 2026 - 23:43

score 224 · Answer 6 · 2026-04-13 10:27:59

224

Views

$\inf(A+B) \geq \inf(A)+\inf(B)$, proving inequality holds?

Published on 13 Apr 2026 - 10:27

score 818 · Answer 7 · 2026-04-13 00:17:48

818

Views

If $\mu $ is mutually singular with $\nu$ and absolutely continuous with respect to $\nu$, show that $\mu=0$

Published on 13 Apr 2026 - 0:17

score 3.9k · Answer 8 · 2026-04-16 07:27:09

3.9k

Views

Find all $n \in \mathbb{Z^+}$ such that $\phi(n)=4$

Published on 16 Apr 2026 - 7:27

score 915 · Answer 9 · 2026-04-25 15:48:46

915

Views

A simple proof that there exixsts lebesgue measurable sets, not borel measurable

Published on 25 Apr 2026 - 15:48

score 49 · Answer 10 · 2026-04-13 16:06:56

49

Views

Is this measurability arguement correct?

Published on 13 Apr 2026 - 16:06

score 59 · Answer 11 · 2026-04-17 12:21:20

59

Views

Proving that if a partition has a limit $a$, then the sequence itself has a limit $a$.

Published on 17 Apr 2026 - 12:21

score 78 · Answer 12 · 2026-04-15 01:21:37

78

Views

If there are $5$ women and $5$ men, how many possibilities exist to form a committee of $3$ women and $2$ men.

Published on 15 Apr 2026 - 1:21

score 282 · Answer 13 · 2026-04-14 22:41:29

282

Views

Proof: $\lim\limits_{n\to\infty}\frac{\sqrt[n]{n!}}{n}=e^{-1}$

Published on 14 Apr 2026 - 22:41

score 31.5k · Answer 14 · 2026-04-14 06:25:34

31.5k

Views

The closure of a set is closed

Published on 14 Apr 2026 - 6:25

score 2.2k · Answer 15 · 2026-04-15 16:17:21

2.2k

Views

If $f$ is holomorphic except for $z_0$, then $\lim_{n\to\infty} \frac{a_n}{a_{n+1}}=z_0$

Published on 15 Apr 2026 - 16:17

List Question

Is there a mistake in this proof of Hall's theorem?

Transformation of a linear independent set is linearly independent

Let $(G, \cdot)$ be a group with the property that there exists $a \in G$ such that $x^3 = xax$, $\forall x \in G$. Prove $G$ is abelian.

Applying Cauchy's integral formula

Homeomorphism $f : (–1,1) \rightarrow \mathbb{R}$

$\inf(A+B) \geq \inf(A)+\inf(B)$, proving inequality holds?

If $\mu $ is mutually singular with $\nu$ and absolutely continuous with respect to $\nu$, show that $\mu=0$

Find all $n \in \mathbb{Z^+}$ such that $\phi(n)=4$

A simple proof that there exixsts lebesgue measurable sets, not borel measurable

Is this measurability arguement correct?

Proving that if a partition has a limit $a$, then the sequence itself has a limit $a$.

If there are $5$ women and $5$ men, how many possibilities exist to form a committee of $3$ women and $2$ men.

Proof: $\lim\limits_{n\to\infty}\frac{\sqrt[n]{n!}}{n}=e^{-1}$

The closure of a set is closed

If $f$ is holomorphic except for $z_0$, then $\lim_{n\to\infty} \frac{a_n}{a_{n+1}}=z_0$

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