Question

Prove that if $(z_n)_{n\geq 1}$ is a null sequence, then $(|z_n|^q)_{n\geq 1}$ with $\forall q\in \mathbb{Q}:q>0$ is a null sequence and vice versa.

score 41 · Answer 1 · 2026-04-15 02:43:03

41

Views

Prove that if $(z_n)_{n\geq 1}$ is a null sequence, then $(|z_n|^q)_{n\geq 1}$ with $\forall q\in \mathbb{Q}:q>0$ is a null sequence and vice versa.

Published on 15 Apr 2026 - 2:43

score 121 · Answer 2 · 2026-04-13 03:23:46

121

Views

Finding Particular Intergrals for ODE's, Is it okay if particular integral varies?

Published on 13 Apr 2026 - 3:23

score 335 · Answer 3 · 2026-04-15 13:11:21

335

Views

Homotopy equivalence upper triangular matrices and torus

Published on 15 Apr 2026 - 13:11

score 850 · Answer 4 · 2026-04-15 03:34:41

850

Views

Differentiability of $f(x,y)=\sqrt{|xy|}$ at $(0,0)$

Published on 15 Apr 2026 - 3:34

score 72 · Answer 5 · 2026-04-13 19:08:00

72

Views

Prove for $k\in \mathbb{Z}$ that $\lim\limits_{n\to\infty}\sqrt[n]{n^k}=1$

Published on 13 Apr 2026 - 19:08

score 304 · Answer 6 · 2026-04-15 17:36:53

304

Views

$(Y,d)$ is a complete metric space $\rightarrow$ $(B(X,Y),p)$ is a complete metric space.

Published on 15 Apr 2026 - 17:36

score 780 · Answer 7 · 2026-04-15 05:05:17

780

Views

If $G$ is a non-abelian finite group, then $|Z(G)| \leq \frac {1}{4} |G|$

Published on 15 Apr 2026 - 5:05

score 5.8k · Answer 8 · 2026-05-11 01:38:07

5.8k

Views

Does the 0th percentile exist?

Published on 11 May 2026 - 1:38

score 138 · Answer 9 · 2026-04-14 09:13:47

138

Views

A prime ideal $P$ contains a minimal prime ideal for any ideal $I \subset P$.

Published on 14 Apr 2026 - 9:13

score 98 · Answer 10 · 2026-04-30 09:46:28

98

Views

Every set in $L(\mathbb{R})$ is $^{\omega}On\text{-definable}$

Published on 30 Apr 2026 - 9:46

score 110 · Answer 11 · 2026-04-16 07:05:27

110

Views

Do independent increments and continuous variance imply that random process is $L_2$ continuous?

Published on 16 Apr 2026 - 7:05

score 57 · Answer 12 · 2026-04-14 23:26:12

57

Views

Is it possible to write any integer $p^n (n\in \mathbb{N})$ in the form $6m\pm 1$.

Published on 14 Apr 2026 - 23:26

score 590 · Answer 13 · 2026-05-03 08:10:06

590

Views

Showing that the set $\{e^{-x}: x > 0, x\in \mathbb{R}\}$ is neither open or closed rigourously.

Published on 03 May 2026 - 8:10

score 75 · Answer 14 · 2026-04-14 15:20:40

75

Views

Prove : For $k\in \mathbb{Z}: \lim\limits_{n\to\infty}\sqrt[n]{n^k}=1$

Published on 14 Apr 2026 - 15:20

score 88 · Answer 15 · 2026-04-16 10:35:25

88

Views

Solve the equation: $x-a^2x-\frac{b^2}{b^2-x^2}+a=\frac{x^2}{x^2-b^2}$

Published on 16 Apr 2026 - 10:35

List Question

Prove that if $(z_n)_{n\geq 1}$ is a null sequence, then $(|z_n|^q)_{n\geq 1}$ with $\forall q\in \mathbb{Q}:q>0$ is a null sequence and vice versa.

Finding Particular Intergrals for ODE's, Is it okay if particular integral varies?

Homotopy equivalence upper triangular matrices and torus

Differentiability of $f(x,y)=\sqrt{|xy|}$ at $(0,0)$

Prove for $k\in \mathbb{Z}$ that $\lim\limits_{n\to\infty}\sqrt[n]{n^k}=1$

$(Y,d)$ is a complete metric space $\rightarrow$ $(B(X,Y),p)$ is a complete metric space.

If $G$ is a non-abelian finite group, then $|Z(G)| \leq \frac {1}{4} |G|$

Does the 0th percentile exist?

A prime ideal $P$ contains a minimal prime ideal for any ideal $I \subset P$.

Every set in $L(\mathbb{R})$ is $^{\omega}On\text{-definable}$

Do independent increments and continuous variance imply that random process is $L_2$ continuous?

Is it possible to write any integer $p^n (n\in \mathbb{N})$ in the form $6m\pm 1$.

Showing that the set $\{e^{-x}: x > 0, x\in \mathbb{R}\}$ is neither open or closed rigourously.

Prove : For $k\in \mathbb{Z}: \lim\limits_{n\to\infty}\sqrt[n]{n^k}=1$

Solve the equation: $x-a^2x-\frac{b^2}{b^2-x^2}+a=\frac{x^2}{x^2-b^2}$

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