Question

Proving a Hausdorff space is a $T_1$-space

score 94 · Answer 1 · 2018-10-20 14:55:47

94

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Proving a Hausdorff space is a $T_1$-space

Published on 20 Oct 2018 - 14:55

score 66 · Answer 2 · 2026-04-02 14:49:35

66

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if $\{a_n\}$ is a sequence such that $a_n \in [c,b]$ and $a_n \rightarrow a$ then $a \in [c,b]$ not understanding the contradiction

Published on 02 Apr 2026 - 14:49

score 195 · Answer 3 · 2026-04-07 21:24:50

195

Views

Given that $\{a_n\}$ is a sequence of $\mathbb{R}$ s.t. $a_n \leq b_n$ and $a_n \rightarrow a$ and $b_n \rightarrow b$ then $a \leq b$

Published on 07 Apr 2026 - 21:24

score 708 · Answer 4 · 2026-04-12 09:53:53

708

Views

Proof of convexity of linear least squares with convexity properties

Published on 12 Apr 2026 - 9:53

score 926 · Answer 5 · 2026-04-02 14:49:41

926

Views

Proving that if $x^4 + 5x + 1 < 27$ then $x < 2$

Published on 02 Apr 2026 - 14:49

score 723 · Answer 6 · 2026-03-25 21:54:04

723

Views

Let $(x_n)$ be Cauchy with a subsequence $(x_{n_k})$ such that $\lim_{k\to\infty} (x_{n_k}) = a$. Show that $\lim_{n\to\infty} (x_{n}) = a$

Published on 25 Mar 2026 - 21:54

score 1.1k · Answer 7 · 2026-03-25 21:49:57

1.1k

Views

Let $(a_n)$ be a sequence such that $\lim_{N\rightarrow \infty} \sum_{n=1}^N |a_n - a_{n+1}| < \infty$. Show that $(a_n)$ is Cauchy.

Published on 25 Mar 2026 - 21:49

score 75 · Answer 8 · 2026-04-12 12:25:45

75

Views

Proof by induction help $\sum_{i=1}^n i2^i$

Published on 12 Apr 2026 - 12:25

score 3.9k · Answer 9 · 2026-04-12 02:42:49

3.9k

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If $H$ and $K$ are normal subgroups of $G$ and $H\bigcap K = \{e\}$, prove that $G$ is isomorphic to a subgroup of $G/H \times G/K$

Published on 12 Apr 2026 - 2:42

score 248 · Answer 10 · 2026-04-09 02:40:44

248

Views

How to simplify nested radicals?

Published on 09 Apr 2026 - 2:40

score 69 · Answer 11 · 2026-04-07 21:23:21

69

Views

If $\{a_n\}$ is a sequence in which $a_n \geq c$ for some constant $c$ and $a_n \rightarrow a$ then $a \geq c$

Published on 07 Apr 2026 - 21:23

score 88 · Answer 12 · 2026-04-13 07:37:42

88

Views

$X\times Y$ homeomorphic to $X^{} \times Y^{}$ Proof Verification

Published on 13 Apr 2026 - 7:37

score 76 · Answer 13 · 2026-03-27 04:21:02

76

Views

Evaluate $\int_0^{\infty}\frac{\cos(3x)}{x^2+12} \ dx$ using resiude theory.

Published on 27 Mar 2026 - 4:21

score 156 · Answer 14 · 2026-04-10 22:44:24

156

Views

In a ring with no nilpotent elements (0) is not decomposable.

Published on 10 Apr 2026 - 22:44

score 87 · Answer 15 · 2026-03-27 00:03:40

87

Views

Prove $\frac{2^{4n}-(-1)^n}{17} \in \mathbb{N}$ by induction

Published on 27 Mar 2026 - 0:03

List Question

Proving a Hausdorff space is a $T_1$-space

if $\{a_n\}$ is a sequence such that $a_n \in [c,b]$ and $a_n \rightarrow a$ then $a \in [c,b]$ not understanding the contradiction

Given that $\{a_n\}$ is a sequence of $\mathbb{R}$ s.t. $a_n \leq b_n$ and $a_n \rightarrow a$ and $b_n \rightarrow b$ then $a \leq b$

Proof of convexity of linear least squares with convexity properties

Proving that if $x^4 + 5x + 1 < 27$ then $x < 2$

Let $(x_n)$ be Cauchy with a subsequence $(x_{n_k})$ such that $\lim_{k\to\infty} (x_{n_k}) = a$. Show that $\lim_{n\to\infty} (x_{n}) = a$

Let $(a_n)$ be a sequence such that $\lim_{N\rightarrow \infty} \sum_{n=1}^N |a_n - a_{n+1}| < \infty$. Show that $(a_n)$ is Cauchy.

Proof by induction help $\sum_{i=1}^n i2^i$

If $H$ and $K$ are normal subgroups of $G$ and $H\bigcap K = \{e\}$, prove that $G$ is isomorphic to a subgroup of $G/H \times G/K$

How to simplify nested radicals?

If $\{a_n\}$ is a sequence in which $a_n \geq c$ for some constant $c$ and $a_n \rightarrow a$ then $a \geq c$

$X\times Y$ homeomorphic to $X^{} \times Y^{}$ Proof Verification

Evaluate $\int_0^{\infty}\frac{\cos(3x)}{x^2+12} \ dx$ using resiude theory.

In a ring with no nilpotent elements (0) is not decomposable.

Prove $\frac{2^{4n}-(-1)^n}{17} \in \mathbb{N}$ by induction

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