Question

Give an example of a non-abelian group $G$ such that $H = \{a \in G \mid\operatorname{ord}(a) < \infty\}$ is not a subgroup of $G$.

score 302 · Answer 1 · 2026-03-29 08:15:59

302

Views

Give an example of a non-abelian group $G$ such that $H = \{a \in G \mid\operatorname{ord}(a) < \infty\}$ is not a subgroup of $G$.

Published on 29 Mar 2026 - 8:15

score 154 · Answer 2 · 2026-03-26 02:34:47

154

Views

Both primal and dual have a unique optimal solution. Something wrong in the assumption/theorem/example?

Published on 26 Mar 2026 - 2:34

score 119 · Answer 3 · 2019-10-16 14:33:20

119

Views

Prove inequality $|y \ln{y} - x \ln{x}| < 2 |\ln{\frac{1}{|y-x|}}|$ when $x,y \in (0,1]$, $x \neq y$.

Published on 16 Oct 2019 - 14:33

score 399 · Answer 4 · 2026-03-28 10:35:22

399

Views

Intersections of saturated locally free sheaves

Published on 28 Mar 2026 - 10:35

score 44 · Answer 5 · 2019-10-17 03:13:18

44

Views

Finding a nonempty perfect set with no rationals

Published on 17 Oct 2019 - 3:13

score 246 · Answer 6 · 2019-10-17 14:52:06

246

Views

What are some counterintuitive results that are really simple to explain?

Published on 17 Oct 2019 - 14:52

score 56 · Answer 7 · 2019-10-18 10:33:26

56

Views

Counterexample of $\lim_{x \to a^+} {1 \over f(x)} = 0$ iff $\lim_{x \to a^+} f(x) = \infty$

Published on 18 Oct 2019 - 10:33

score 59 · Answer 8 · 2019-10-18 14:41:32

59

Views

show this inequality if $\sum_{1\le i<j\le n}a_{i}a_{j}=\binom{n}{2}$

Published on 18 Oct 2019 - 14:41

score 137 · Answer 9 · 2026-02-23 19:40:15

137

Views

Elaborating an example that shows that pointwise convergence is not sufficient to pass the limit under the integral sign.

Published on 23 Feb 2026 - 19:40

score 136 · Answer 10 · 2019-10-19 17:38:09

136

Views

Counterexample of bounded variation function $f$

Published on 19 Oct 2019 - 17:38

score 67 · Answer 11 · 2019-10-21 17:19:30

67

Views

Understanding an example on pg.83 (Royden $4^{th}$ edition).

Published on 21 Oct 2019 - 17:19

score 36 · Answer 12 · 2019-10-21 17:41:18

36

Views

Counter Example for a couple for random variables $(U,V)$ and $(X,Y).$

Published on 21 Oct 2019 - 17:41

score 54 · Answer 13 · 2019-10-21 23:15:16

54

Views

An elaboration of a second example of strict inequality in Fatou's lemma (pg.83 Royen $4^{th}$ edition).

Published on 21 Oct 2019 - 23:15

score 81 · Answer 14 · 2026-02-23 19:36:35

81

Views

Sequence of functions converges

Published on 23 Feb 2026 - 19:36

score 93 · Answer 15 · 2026-03-26 19:01:56

93

Views

$0\rightarrow \mathbb{Z} \xrightarrow{ f_k} \mathbb{Z}\ \xrightarrow{ \pi } \mathbb{Z}/{k \mathbb{Z} } \rightarrow 0.$ is exact but not split

Published on 26 Mar 2026 - 19:01

List Question

Give an example of a non-abelian group $G$ such that $H = \{a \in G \mid\operatorname{ord}(a) < \infty\}$ is not a subgroup of $G$.

Both primal and dual have a unique optimal solution. Something wrong in the assumption/theorem/example?

Prove inequality $|y \ln{y} - x \ln{x}| < 2 |\ln{\frac{1}{|y-x|}}|$ when $x,y \in (0,1]$, $x \neq y$.

Intersections of saturated locally free sheaves

Finding a nonempty perfect set with no rationals

What are some counterintuitive results that are really simple to explain?

Counterexample of $\lim_{x \to a^+} {1 \over f(x)} = 0$ iff $\lim_{x \to a^+} f(x) = \infty$

show this inequality if $\sum_{1\le i<j\le n}a_{i}a_{j}=\binom{n}{2}$

Elaborating an example that shows that pointwise convergence is not sufficient to pass the limit under the integral sign.

Counterexample of bounded variation function $f$

Understanding an example on pg.83 (Royden $4^{th}$ edition).

Counter Example for a couple for random variables $(U,V)$ and $(X,Y).$

An elaboration of a second example of strict inequality in Fatou's lemma (pg.83 Royen $4^{th}$ edition).

Sequence of functions converges

$0\rightarrow \mathbb{Z} \xrightarrow{ f_k} \mathbb{Z}\ \xrightarrow{ \pi } \mathbb{Z}/{k \mathbb{Z} } \rightarrow 0.$ is exact but not split

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