Question

Prove/show that $\epsilon_{ijk}(\hat a_j \hat b_k-\hat b_k \hat a_j)=2\epsilon_{ijk}\hat a_j\hat b_k$

score 211 · Answer 1 · 2026-04-16 20:48:39

211

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Prove/show that $\epsilon_{ijk}(\hat a_j \hat b_k-\hat b_k \hat a_j)=2\epsilon_{ijk}\hat a_j\hat b_k$

Published on 16 Apr 2026 - 20:48

score 104 · Answer 2 · 2026-05-11 08:19:07

104

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Show that $\sum_{(n,m)\in A\times B}x_{n,m}=\sum_{n\in A}\sum_{m\in B}x_{n,m}=\sum_{m\in B}\sum_{n\in A}x_{n,m}.$ Tao's Introduction to Measure Theory

Published on 11 May 2026 - 8:19

score 59 · Answer 3 · 2026-04-15 20:56:53

59

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Equivalent metrics on compact metric space

Published on 15 Apr 2026 - 20:56

score 84 · Answer 4 · 2026-04-11 08:18:43

84

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Proof: It is not true that if a partially ordered set has exactly one minimal element, then it must be the smallest element.

Published on 11 Apr 2026 - 8:18

score 130 · Answer 5 · 2026-04-14 22:03:04

130

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Let $n \in \mathbb {N}$ and $G$ a group of order $4n+2$. Prove $G$ isn't simple.

Published on 14 Apr 2026 - 22:03

score 185 · Answer 6 · 2026-04-09 13:43:17

185

Views

Question about Rudin's PMA, Chapter 2 Exercise 2

Published on 09 Apr 2026 - 13:43

score 56 · Answer 7 · 2026-04-14 05:28:46

56

Views

Using the least upper bound property of real numbers prove that every closed interval $[a,b]\space (a\lt b)$ is compact.

Published on 14 Apr 2026 - 5:28

score 169 · Answer 8 · 2026-05-10 19:48:11

169

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Exercise 3, Section 1.5 of Hungerford’s Abstract Algebra

Published on 10 May 2026 - 19:48

score 278 · Answer 9 · 2026-04-17 11:03:00

278

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Let $f:(a,b) \to \mathbb R$ differentiable s.t $f^{'}(x) \ge 0$ in $(a,b)$ and $f^{'} = 0$ only in one coordinate. Prove $f$ is strictly increasing.

Published on 17 Apr 2026 - 11:03

score 56 · Answer 10 · 2026-04-16 13:30:54

56

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Define the closure of a set $A\subset \Bbb R$ as $clA.$ Show that $x\in clA,$ iff $d(x,A)=0$ where $d(x,A)=inf\{|x-a|:a\in A\}.$

Published on 16 Apr 2026 - 13:30

score 61 · Answer 11 · 2026-04-13 12:19:35

61

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Isolated singularities of $\sin(1/(\sin(1/z)))$ using Casorati-Weierstrass

Published on 13 Apr 2026 - 12:19

score 207 · Answer 12 · 2026-04-16 05:45:23

207

Views

Proving $2\sin x\cos x = \sin 2x$

Published on 16 Apr 2026 - 5:45

score 41 · Answer 13 · 2026-04-15 12:28:58

41

Views

Suppose $R$ is a relation on $A$. Let $S$ be the transitive closure of $R$. Then $Dom(S)\subset Dom(R)$

Published on 15 Apr 2026 - 12:28

score 37 · Answer 14 · 2026-04-16 15:38:31

37

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Show that this set is $\Pi_1^0$-complete?

Published on 16 Apr 2026 - 15:38

score 26 · Answer 15 · 2026-04-28 20:21:40

26

Views

Prove Lebesgue measurability of a pieceswise function $f(x,y)$

Published on 28 Apr 2026 - 20:21

List Question

Prove/show that $\epsilon_{ijk}(\hat a_j \hat b_k-\hat b_k \hat a_j)=2\epsilon_{ijk}\hat a_j\hat b_k$

Show that $\sum_{(n,m)\in A\times B}x_{n,m}=\sum_{n\in A}\sum_{m\in B}x_{n,m}=\sum_{m\in B}\sum_{n\in A}x_{n,m}.$ Tao's Introduction to Measure Theory

Equivalent metrics on compact metric space

Proof: It is not true that if a partially ordered set has exactly one minimal element, then it must be the smallest element.

Let $n \in \mathbb {N}$ and $G$ a group of order $4n+2$. Prove $G$ isn't simple.

Question about Rudin's PMA, Chapter 2 Exercise 2

Using the least upper bound property of real numbers prove that every closed interval $[a,b]\space (a\lt b)$ is compact.

Exercise 3, Section 1.5 of Hungerford’s Abstract Algebra

Let $f:(a,b) \to \mathbb R$ differentiable s.t $f^{'}(x) \ge 0$ in $(a,b)$ and $f^{'} = 0$ only in one coordinate. Prove $f$ is strictly increasing.

Define the closure of a set $A\subset \Bbb R$ as $clA.$ Show that $x\in clA,$ iff $d(x,A)=0$ where $d(x,A)=inf\{|x-a|:a\in A\}.$

Isolated singularities of $\sin(1/(\sin(1/z)))$ using Casorati-Weierstrass

Proving $2\sin x\cos x = \sin 2x$

Suppose $R$ is a relation on $A$. Let $S$ be the transitive closure of $R$. Then $Dom(S)\subset Dom(R)$

Show that this set is $\Pi_1^0$-complete?

Prove Lebesgue measurability of a pieceswise function $f(x,y)$

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