Question

If $(x^{(n)})^∞_{n=m}$ is Cauchy and if some subsequence of $(x^{(n)})^∞_{n=m}$ converges then so does $(x^{(n)})^∞_{n=m}$

score 58 · Answer 1 · 2026-04-09 15:44:13

58

Views

If $(x^{(n)})^∞_{n=m}$ is Cauchy and if some subsequence of $(x^{(n)})^∞_{n=m}$ converges then so does $(x^{(n)})^∞_{n=m}$

Published on 09 Apr 2026 - 15:44

score 100 · Answer 2 · 2026-04-10 05:35:58

100

Views

Proof verification: $\forall n \in \mathbb{Z}, 4\nmid(n^2+2)$

Published on 10 Apr 2026 - 5:35

score 339 · Answer 3 · 2026-04-09 02:39:01

339

Views

Hilbert's style sysytem without deductive theorem.

Published on 09 Apr 2026 - 2:39

score 178 · Answer 4 · 2026-04-01 05:06:24

178

Views

Showing that a limit point $L$ of $(x^{(n)})^∞_{n=m}$ and a subsequence of $(x^{(n)})^∞_{n=m}$ which converges to L are equal

Published on 01 Apr 2026 - 5:06

score 470 · Answer 5 · 2018-01-24 21:11:32

470

Views

Intersection of a sequence of closed intervals

Published on 24 Jan 2018 - 21:11

score 2.8k · Answer 6 · 2026-03-25 04:40:12

2.8k

Views

Proof that a factorization domain is a unique factorization domain if and only if every irreducible element is prime.

Published on 25 Mar 2026 - 4:40

score 494 · Answer 7 · 2026-04-09 01:44:06

494

Views

Inductive proof on a sequence

Published on 09 Apr 2026 - 1:44

score 159 · Answer 8 · 2026-04-08 22:42:42

159

Views

Trouble with a proof. I cannot prove this without inf many proofs for each and every case.

Published on 08 Apr 2026 - 22:42

score 1.5k · Answer 9 · 2026-03-25 05:41:28

1.5k

Views

Proof of cancellation law for vector addition

Published on 25 Mar 2026 - 5:41

score 143 · Answer 10 · 2026-03-25 11:16:32

143

Views

Proof verification : $n\cdot \int_{0}^{1} x^n \cdot f(x) \, \mathrm{d}x\underset{n\to+\infty}{\longrightarrow}f(1) $

Published on 25 Mar 2026 - 11:16

score 171 · Answer 11 · 2026-03-26 02:45:52

171

Views

Prove that, $\binom{3n}{r}=\binom{3n-1}{r} + \binom{3n-1}{r-1}$

Published on 26 Mar 2026 - 2:45

score 257 · Answer 12 · 2026-04-06 10:39:42

257

Views

Prove sup, inf max and min of set

Published on 06 Apr 2026 - 10:39

score 781 · Answer 13 · 2026-03-25 05:46:58

781

Views

Proving that a sequence converges to L

Published on 25 Mar 2026 - 5:46

score 115 · Answer 14 · 2026-03-25 12:33:07

115

Views

Let G= (V; E) be a graph. Prove that G is a connected graph

Published on 25 Mar 2026 - 12:33

score 1k · Answer 15 · 2026-04-06 19:31:47

1k

Views

Recursive proof by induction with pseudocode

Published on 06 Apr 2026 - 19:31

List Question

If $(x^{(n)})^∞_{n=m}$ is Cauchy and if some subsequence of $(x^{(n)})^∞_{n=m}$ converges then so does $(x^{(n)})^∞_{n=m}$

Proof verification: $\forall n \in \mathbb{Z}, 4\nmid(n^2+2)$

Hilbert's style sysytem without deductive theorem.

Showing that a limit point $L$ of $(x^{(n)})^∞_{n=m}$ and a subsequence of $(x^{(n)})^∞_{n=m}$ which converges to L are equal

Intersection of a sequence of closed intervals

Proof that a factorization domain is a unique factorization domain if and only if every irreducible element is prime.

Inductive proof on a sequence

Trouble with a proof. I cannot prove this without inf many proofs for each and every case.

Proof of cancellation law for vector addition

Proof verification : $n\cdot \int_{0}^{1} x^n \cdot f(x) \, \mathrm{d}x\underset{n\to+\infty}{\longrightarrow}f(1) $

Prove that, $\binom{3n}{r}=\binom{3n-1}{r} + \binom{3n-1}{r-1}$

Prove sup, inf max and min of set

Proving that a sequence converges to L

Let G= (V; E) be a graph. Prove that G is a connected graph

Recursive proof by induction with pseudocode

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