Question

Proving there are no rational cubic roots between two $f^3$ and $(f+1)^3$

score 77 · Answer 1 · 2026-04-16 15:18:18

77

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Proving there are no rational cubic roots between two $f^3$ and $(f+1)^3$

Published on 16 Apr 2026 - 15:18

score 62 · Answer 2 · 2026-05-11 02:04:32

62

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Prove every point on the plane is a unique affine combination of the vertices of any triangle

Published on 11 May 2026 - 2:04

score 99 · Answer 3 · 2026-04-13 02:58:52

99

Views

Solving biharmonic equation for $\mathbb{R}^2$

Published on 13 Apr 2026 - 2:58

score 155 · Answer 4 · 2026-04-16 00:58:17

155

Views

Let $x$ be a rational number. Prove that if the product $xy$ is irrational, then $y$ is irrational.

Published on 16 Apr 2026 - 0:58

score 209 · Answer 5 · 2026-04-15 13:32:53

209

Views

Differentiability of $f(x,y) = |xy|$

Published on 15 Apr 2026 - 13:32

score 35 · Answer 6 · 2026-04-14 13:36:17

35

Views

Assume $T\in \mathcal L(E, F)$. Then $T\in \mathcal K(E, F)$ IFF $T^* \in \mathcal K(F^, E^)$

Published on 14 Apr 2026 - 13:36

score 68 · Answer 7 · 2026-04-17 03:29:36

68

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Let $G=P\rtimes Q,P=\Bbb Z_7=\langle b\rangle,Q=\Bbb Z_3=\langle a\rangle.$ Let $\theta:Q\to{\rm Aut}P$ be $\theta(a)(b)=b^4$. Classify $G/G'$.

Published on 17 Apr 2026 - 3:29

score 56 · Answer 8 · 2026-04-14 11:53:43

56

Views

In $\left(C([0,1]), d_{\infty}\right)$, the subset $ A=\{f \in C([0,1]): f(t)>t, \forall t \in[0,1]\}$ is open

Published on 14 Apr 2026 - 11:53

score 81 · Answer 9 · 2026-04-14 11:45:50

81

Views

If $a>0, b>0$, then $\frac{a}{b}+\frac{b}{a}\geq2$.

Published on 14 Apr 2026 - 11:45

score 40 · Answer 10 · 2026-04-11 01:44:34

40

Views

Homotopy equivalence of disjoint union preserved under 'universal property'

Published on 11 Apr 2026 - 1:44

score 44 · Answer 11 · 2026-04-17 14:02:13

44

Views

Study the convergence of the sequence $u_n = 5 - \frac{8}{5}n$

Published on 17 Apr 2026 - 14:02

score 116 · Answer 12 · 2026-04-12 15:17:08

116

Views

Is my solution ok? Exercise 5 on p.85 in Exercises 3A in "Measure, Integration & Real Analysis" by Sheldon Axler.

Published on 12 Apr 2026 - 15:17

score 145 · Answer 13 · 2026-04-15 12:42:29

145

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Proving $\lim_{n\to\infty}f_n(x)$ doesn't exist for any $x\in[0,1],$ where $(f_n)_{n\in\Bbb N}$ is the Typewriter sequence

Published on 15 Apr 2026 - 12:42

score 156 · Answer 14 · 2026-04-15 10:58:00

156

Views

If $G$ has finite codimension, then $G$ has a complement

Published on 15 Apr 2026 - 10:58

score 39 · Answer 15 · 2026-04-10 07:29:21

39

Views

Proof verification: The mappings set between two sets is a set

Published on 10 Apr 2026 - 7:29

List Question

Proving there are no rational cubic roots between two $f^3$ and $(f+1)^3$

Prove every point on the plane is a unique affine combination of the vertices of any triangle

Solving biharmonic equation for $\mathbb{R}^2$

Let $x$ be a rational number. Prove that if the product $xy$ is irrational, then $y$ is irrational.

Differentiability of $f(x,y) = |xy|$

Assume $T\in \mathcal L(E, F)$. Then $T\in \mathcal K(E, F)$ IFF $T^* \in \mathcal K(F^, E^)$

Let $G=P\rtimes Q,P=\Bbb Z_7=\langle b\rangle,Q=\Bbb Z_3=\langle a\rangle.$ Let $\theta:Q\to{\rm Aut}P$ be $\theta(a)(b)=b^4$. Classify $G/G'$.

In $\left(C([0,1]), d_{\infty}\right)$, the subset $ A=\{f \in C([0,1]): f(t)>t, \forall t \in[0,1]\}$ is open

If $a>0, b>0$, then $\frac{a}{b}+\frac{b}{a}\geq2$.

Homotopy equivalence of disjoint union preserved under 'universal property'

Study the convergence of the sequence $u_n = 5 - \frac{8}{5}n$

Is my solution ok? Exercise 5 on p.85 in Exercises 3A in "Measure, Integration & Real Analysis" by Sheldon Axler.

Proving $\lim_{n\to\infty}f_n(x)$ doesn't exist for any $x\in[0,1],$ where $(f_n)_{n\in\Bbb N}$ is the Typewriter sequence

If $G$ has finite codimension, then $G$ has a complement

Proof verification: The mappings set between two sets is a set

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