Question

Suppose $G$ is a finite group and $|G:H|=n$ I want to show that $|H:H\cap H^g|\leq n$ for all $g\in G$.

score 168 · Answer 1 · 2026-04-15 18:53:53

168

Views

Suppose $G$ is a finite group and $|G:H|=n$ I want to show that $|H:H\cap H^g|\leq n$ for all $g\in G$.

Published on 15 Apr 2026 - 18:53

score 98 · Answer 2 · 2026-04-19 14:05:11

98

Views

Brezis' exercise 6.19: prove that $\sigma(T) = \sigma(T^*)$

Published on 19 Apr 2026 - 14:05

score 75 · Answer 3 · 2026-04-16 04:56:30

75

Views

When is a proof too vague? (If $r_1,r_2,\ldots,r_n$ are roots of polynomial $p$ with leading term $x^n$, then $r_1+r_2+\cdots+r_n=(-1)a_{n-1}$)

Published on 16 Apr 2026 - 4:56

score 41 · Answer 4 · 2026-05-15 17:06:56

41

Views

Brezis' exercise 6.20.1: prove that $T \in \mathcal{K}(E)$

Published on 15 May 2026 - 17:06

score 68 · Answer 5 · 2026-04-15 21:08:41

68

Views

Brezis' exercise 6.20.2: prove that $0 \notin EV(T)$

Published on 15 Apr 2026 - 21:08

score 191 · Answer 6 · 2026-04-13 20:49:40

191

Views

Password formation - Combinatorics

Published on 13 Apr 2026 - 20:49

score 59 · Answer 7 · 2026-05-16 11:27:56

59

Views

If a functor commutes with all filtered colimits, then does it commute with all existing colimits?

Published on 16 May 2026 - 11:27

score 116 · Answer 8 · 2026-04-14 21:32:36

116

Views

Brezis' exercise 6.20.2: prove that $\sigma (T) = \{0\}$

Published on 14 Apr 2026 - 21:32

score 264 · Answer 9 · 2026-04-13 17:00:41

264

Views

Is my proof of $1+1=2$ correct?

Published on 13 Apr 2026 - 17:00

score 49 · Answer 10 · 2026-05-16 04:49:11

49

Views

Let $f(x,y)=x+y$ and $g(x,y)=xy$, prove that the closure of $\mathbb{Q} \cup\{\sqrt{2}\}$ under $\{f, g\}$ is $\mathbb{Q}(\sqrt{2})$

Published on 16 May 2026 - 4:49

score 30 · Answer 11 · 2026-04-14 23:44:41

30

Views

Proving the differential of $y\mapsto\int_b^aF(x,y,y')\ dx$ is given by $h\mapsto\int_b^a\left[F_y(x,y,y')h+F_{y'}(x,y,y')h'\right]\ dx$

Published on 14 Apr 2026 - 23:44

score 64 · Answer 12 · 2026-04-15 13:29:28

64

Views

Brezis' exercise 6.20.3: give an explicit formula for $(T-\lambda I)^{-1}$

Published on 15 Apr 2026 - 13:29

score 42 · Answer 13 · 2026-04-13 06:52:56

42

Views

Showing that adding by $1$ is the same as the successor function

Published on 13 Apr 2026 - 6:52

score 37 · Answer 14 · 2026-04-15 11:18:40

37

Views

Brezis' exercise 6.20.4: determine $T^*$

Published on 15 Apr 2026 - 11:18

score 75 · Answer 15 · 2026-04-16 19:32:06

75

Views

if f,g are both measurable functions whose range is $\mathbb{R}^+$ then $\int_X g d\varphi = \int_X fgd\mu$

Published on 16 Apr 2026 - 19:32

List Question

Suppose $G$ is a finite group and $|G:H|=n$ I want to show that $|H:H\cap H^g|\leq n$ for all $g\in G$.

Brezis' exercise 6.19: prove that $\sigma(T) = \sigma(T^*)$

When is a proof too vague? (If $r_1,r_2,\ldots,r_n$ are roots of polynomial $p$ with leading term $x^n$, then $r_1+r_2+\cdots+r_n=(-1)a_{n-1}$)

Brezis' exercise 6.20.1: prove that $T \in \mathcal{K}(E)$

Brezis' exercise 6.20.2: prove that $0 \notin EV(T)$

Password formation - Combinatorics

If a functor commutes with all filtered colimits, then does it commute with all existing colimits?

Brezis' exercise 6.20.2: prove that $\sigma (T) = \{0\}$

Is my proof of $1+1=2$ correct?

Let $f(x,y)=x+y$ and $g(x,y)=xy$, prove that the closure of $\mathbb{Q} \cup\{\sqrt{2}\}$ under $\{f, g\}$ is $\mathbb{Q}(\sqrt{2})$

Proving the differential of $y\mapsto\int_b^aF(x,y,y')\ dx$ is given by $h\mapsto\int_b^a\left[F_y(x,y,y')h+F_{y'}(x,y,y')h'\right]\ dx$

Brezis' exercise 6.20.3: give an explicit formula for $(T-\lambda I)^{-1}$

Showing that adding by $1$ is the same as the successor function

Brezis' exercise 6.20.4: determine $T^*$

if f,g are both measurable functions whose range is $\mathbb{R}^+$ then $\int_X g d\varphi = \int_X fgd\mu$

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