Question

A sequence $\{x_n\}$ is convergent in $\prod X_\alpha$ iff the projection sequence $\{\pi_\alpha(x_n)\}$ converges in $X_\alpha$ for any $\alpha$

score 408 · Answer 1 · 2026-03-26 08:00:41

408

Views

A sequence $\{x_n\}$ is convergent in $\prod X_\alpha$ iff the projection sequence $\{\pi_\alpha(x_n)\}$ converges in $X_\alpha$ for any $\alpha$

Published on 26 Mar 2026 - 8:00

score 1.5k · Answer 2 · 2018-03-11 07:23:01

1.5k

Views

Proof Explanation: Convergence implies boundedness

Published on 11 Mar 2018 - 7:23

score 38 · Answer 3 · 2018-03-11 09:42:30

38

Views

Divergence of the sequence $s_n = n$, i.e., the sequence $1,2,3, \dots n$

Published on 11 Mar 2018 - 9:42

score 1.5k · Answer 4 · 2026-03-22 16:04:58

1.5k

Views

What happened here at the proof of associative law for addition?

Published on 22 Mar 2026 - 16:04

score 44 · Answer 5 · 2018-03-11 10:22:10

44

Views

Find a $N \in I \ni \left|\frac{2n}{n+3} - 3\right| < \frac{1}{5}\,\forall\,n\geq N$

Published on 11 Mar 2018 - 10:22

score 2.9k · Answer 6 · 2026-03-25 16:03:08

2.9k

Views

If $H\leq G$ and $[G:H]=2$, then $H$ is normal in $G$.

Published on 25 Mar 2026 - 16:03

score 259 · Answer 7 · 2026-03-25 05:48:44

259

Views

Proof Explanation: Sequences, convergence

Published on 25 Mar 2026 - 5:48

score 65 · Answer 8 · 2018-03-13 03:46:28

65

Views

Why is a particular element in a normal subgroup of G?

Published on 13 Mar 2018 - 3:46

score 171 · Answer 9 · 2026-03-19 19:06:15

171

Views

Understanding a result of Serre about zeros of $x^3 - x - 1$ in $\mathbb{F}_p$

Published on 19 Mar 2026 - 19:06

score 67 · Answer 10 · 2018-03-13 13:41:06

67

Views

Why proof by contradiction here?

Published on 13 Mar 2018 - 13:41

score 385 · Answer 11 · 2026-03-25 01:17:00

385

Views

Is there a way to prove this inequality for integrals?

Published on 25 Mar 2026 - 1:17

score 786 · Answer 12 · 2026-03-26 22:14:10

786

Views

Can we prove $\sin(x)^2 + \cos(x)^2 = 1$ using just their series?

Published on 26 Mar 2026 - 22:14

score 25 · Answer 13 · 2018-03-14 09:24:26

25

Views

$a^2 |b$ and $b^3 |c$ , prove $a^6 |c$

Published on 14 Mar 2018 - 9:24

score 38 · Answer 14 · 2026-03-24 23:51:11

38

Views

Regrading segments in planar graphs

Published on 24 Mar 2026 - 23:51

score 2.8k · Answer 15 · 2026-03-23 11:34:56

2.8k

Views

How to prove $\ln(x)$ is analytic everywhere?

Published on 23 Mar 2026 - 11:34

List Question

A sequence $\{x_n\}$ is convergent in $\prod X_\alpha$ iff the projection sequence $\{\pi_\alpha(x_n)\}$ converges in $X_\alpha$ for any $\alpha$

Proof Explanation: Convergence implies boundedness

Divergence of the sequence $s_n = n$, i.e., the sequence $1,2,3, \dots n$

What happened here at the proof of associative law for addition?

Find a $N \in I \ni \left|\frac{2n}{n+3} - 3\right| < \frac{1}{5}\,\forall\,n\geq N$

If $H\leq G$ and $[G:H]=2$, then $H$ is normal in $G$.

Proof Explanation: Sequences, convergence

Why is a particular element in a normal subgroup of G?

Understanding a result of Serre about zeros of $x^3 - x - 1$ in $\mathbb{F}_p$

Why proof by contradiction here?

Is there a way to prove this inequality for integrals?

Can we prove $\sin(x)^2 + \cos(x)^2 = 1$ using just their series?

$a^2 |b$ and $b^3 |c$ , prove $a^6 |c$

Regrading segments in planar graphs

How to prove $\ln(x)$ is analytic everywhere?

Trending Questions

Popular # Hahtags

Popular Questions