Question

Exercise about a direct product of modules that is not equal to its direct sum

score 293 · Answer 1 · 2018-01-28 00:55:15

293

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Exercise about a direct product of modules that is not equal to its direct sum

Published on 28 Jan 2018 - 0:55

score 40 · Answer 2 · 2026-03-25 07:21:57

40

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Confirmation of Proof: $\forall\{x,y,z\}\subset\mathbb{Z}, \ x^2 + 2y^2 = 3z^2 \Leftrightarrow 3\mid x\land y$

Published on 25 Mar 2026 - 7:21

score 5.4k · Answer 3 · 2026-03-22 04:09:14

5.4k

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Is this a valid proof? If $a$ and $b$ are rational, $a^b$ is rational.

Published on 22 Mar 2026 - 4:09

score 111 · Answer 4 · 2026-03-25 12:33:53

111

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Equality of finite sets with $A \subseteq B$ and $|A|=|B|$

Published on 25 Mar 2026 - 12:33

score 68 · Answer 5 · 2026-03-22 02:26:43

68

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Multivariable Taylor polynomial when $f(x,y)=xe^{-xy^2}$

Published on 22 Mar 2026 - 2:26

score 268 · Answer 6 · 2018-01-28 11:07:05

268

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Find $F(n,k)$ number of monotonic sequences in length $k$ from $n$ elements $\{1,2,3,..,n\}$

Published on 28 Jan 2018 - 11:07

score 231 · Answer 7 · 2026-03-24 23:42:54

231

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Trigonometry problem, Evaluate: $\frac {1}{\sin 18°}$

Published on 24 Mar 2026 - 23:42

score 55 · Answer 8 · 2018-01-28 15:25:31

55

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alternative proof for limit

Published on 28 Jan 2018 - 15:25

score 199 · Answer 9 · 2026-03-17 03:50:30

199

Views

Proving the area of the circle using sticks.

Published on 17 Mar 2026 - 3:50

score 374 · Answer 10 · 2026-03-25 03:02:28

374

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Irreducible components and flat maps of schemes

Published on 25 Mar 2026 - 3:02

score 94 · Answer 11 · 2026-03-25 06:13:27

94

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Let $f: [0,1] \to R$ be Riemann integrable, and let $a > 0$ be a real number. Show that $ f({x\over a})$ is Riemann integrable on $[0,a]$

Published on 25 Mar 2026 - 6:13

score 68 · Answer 12 · 2026-03-25 06:48:52

68

Views

Is $R$ symmetric and transitive?

Published on 25 Mar 2026 - 6:48

score 220 · Answer 13 · 2026-03-19 21:21:55

220

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Proof check, existence of free product

Published on 19 Mar 2026 - 21:21

score 1k · Answer 14 · 2026-03-24 22:08:49

1k

Views

Proof verification: Prove whether or not every proper subgroup of a nonabelian group is nonabelian.

Published on 24 Mar 2026 - 22:08

score 146 · Answer 15 · 2026-03-24 22:01:56

146

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Let $H\leq G$. If $g\in G$, show that $gHg^{-1}=\left \{ g^{-1}hg:h\in H,g\in G \right \}$ is a subgroup of $G$.

Published on 24 Mar 2026 - 22:01

List Question

Exercise about a direct product of modules that is not equal to its direct sum

Confirmation of Proof: $\forall\{x,y,z\}\subset\mathbb{Z}, \ x^2 + 2y^2 = 3z^2 \Leftrightarrow 3\mid x\land y$

Is this a valid proof? If $a$ and $b$ are rational, $a^b$ is rational.

Equality of finite sets with $A \subseteq B$ and $|A|=|B|$

Multivariable Taylor polynomial when $f(x,y)=xe^{-xy^2}$

Find $F(n,k)$ number of monotonic sequences in length $k$ from $n$ elements $\{1,2,3,..,n\}$

Trigonometry problem, Evaluate: $\frac {1}{\sin 18°}$

alternative proof for limit

Proving the area of the circle using sticks.

Irreducible components and flat maps of schemes

Let $f: [0,1] \to R$ be Riemann integrable, and let $a > 0$ be a real number. Show that $ f({x\over a})$ is Riemann integrable on $[0,a]$

Is $R$ symmetric and transitive?

Proof check, existence of free product

Proof verification: Prove whether or not every proper subgroup of a nonabelian group is nonabelian.

Let $H\leq G$. If $g\in G$, show that $gHg^{-1}=\left \{ g^{-1}hg:h\in H,g\in G \right \}$ is a subgroup of $G$.

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