Question

If $x_n$ converges to $L \in \mathbb{R}$ with $x_n \leq B$ for all $n \in \mathbb{N}$, then $\lim_{n\to\infty} x_n = L \leq B$

score 930 · Answer 1 · 2020-05-14 20:03:41

If $x_n$ converges to $L \in \mathbb{R}$ with $x_n \leq B$ for all $n \in \mathbb{N}$, then $\lim_{n\to\infty} x_n = L \leq B$

score 440 · Answer 2 · 2020-05-14 21:44:54

440

Views

All separable zero-dimensional metric spaces can be embedded into the Cantor set

Published on 14 May 2020 - 21:44

score 186 · Answer 3 · 2026-03-27 10:45:59

186

Views

Find $\text{min}{F_{D}(X)}$ for an arbitrary diagonal matrix

Published on 27 Mar 2026 - 10:45

score 105 · Answer 4 · 2020-05-14 23:38:04

105

Views

Suppose that $A$, $B$ and $C$ are sets, and $A\setminus B\subseteq C$. Show that $A\setminus C\subseteq B$.

Published on 14 May 2020 - 23:38

score 68 · Answer 5 · 2026-04-13 00:02:12

68

Views

Limit points of subsequences of $(a_n)$ are equal to limit points of A?

Published on 13 Apr 2026 - 0:02

score 1k · Answer 6 · 2020-05-14 23:47:20

Show that the sequence $\{a_n\}$ converges where $a_1 = 1$ and $a_n = \sqrt{1+ a_{n-1}}$ for all $n \geq 2$. With MCT and induction.

score 76 · Answer 7 · 2026-04-06 04:59:13

76

Views

Am I proving correctly that the uniform convergence of the product is the product of the limits when each sequence is uniformly bounded?

Published on 06 Apr 2026 - 4:59

score 181 · Answer 8 · 2020-05-15 00:39:58

181

Views

Proof verification: $|X|=|Y|=m \in \mathbb{N}$ there exists exactly $m!$

Published on 15 May 2020 - 0:39

score 359 · Answer 9 · 2020-05-15 02:28:14

359

Views

If every subsequence contains a convergent subsequence, then $(a_n)$ converges to the same limit

Published on 15 May 2020 - 2:28

score 107 · Answer 10 · 2020-05-15 03:32:32

107

Views

Prove that $\left|\int_0^1 f(x)dx\right|\ge 1\text{ or }\left|\int_0^1 g(x)dx\right|\ge 1.$

Published on 15 May 2020 - 3:32

score 98 · Answer 11 · 2026-03-30 02:08:53

98

Views

Writing an $\varepsilon$-$\delta$ proof of $\lim_{x\to a}[f(x)g(x)] = \infty$, given $\lim_{x\to a}f(x)=\infty$, $\lim_{x\to a}g(x)=c>0$

Published on 30 Mar 2026 - 2:08

score 72 · Answer 12 · 2026-04-13 07:09:24

72

Views

Prove that $BQ$ bisects segment $EF$.

Published on 13 Apr 2026 - 7:09

score 69 · Answer 13 · 2026-04-02 06:20:09

69

Views

A field $K$ of order $q=p^r$ contains a subfield $K'$ of order $q'=p^k$ if and only if $k\mid r$.

Published on 02 Apr 2026 - 6:20

score 162 · Answer 14 · 2020-05-15 08:40:21

$f:\mathbb{R}\to\mathbb{R}$ satisfies $f(3x)=3f(x)-4f(x)^3, \forall x\in\mathbb{R}$ and is continuous at $x=0$. Show that $|f(x)|\le 1, \forall x.$

score 115 · Answer 15 · 2020-05-15 08:42:51

115

Views

Prove that $\frac{1}{\sqrt{1-x^2}}$ is unbounded for $x\in(-1,1)$

Published on 15 May 2020 - 8:42

List Question

If $x_n$ converges to $L \in \mathbb{R}$ with $x_n \leq B$ for all $n \in \mathbb{N}$, then $\lim_{n\to\infty} x_n = L \leq B$

All separable zero-dimensional metric spaces can be embedded into the Cantor set

Find $\text{min}{F_{D}(X)}$ for an arbitrary diagonal matrix

Suppose that $A$, $B$ and $C$ are sets, and $A\setminus B\subseteq C$. Show that $A\setminus C\subseteq B$.

Limit points of subsequences of $(a_n)$ are equal to limit points of A?

Show that the sequence $\{a_n\}$ converges where $a_1 = 1$ and $a_n = \sqrt{1+ a_{n-1}}$ for all $n \geq 2$. With MCT and induction.

Am I proving correctly that the uniform convergence of the product is the product of the limits when each sequence is uniformly bounded?

Proof verification: $|X|=|Y|=m \in \mathbb{N}$ there exists exactly $m!$

If every subsequence contains a convergent subsequence, then $(a_n)$ converges to the same limit

Prove that $\left|\int_0^1 f(x)dx\right|\ge 1\text{ or }\left|\int_0^1 g(x)dx\right|\ge 1.$

Writing an $\varepsilon$-$\delta$ proof of $\lim_{x\to a}[f(x)g(x)] = \infty$, given $\lim_{x\to a}f(x)=\infty$, $\lim_{x\to a}g(x)=c>0$

Prove that $BQ$ bisects segment $EF$.

A field $K$ of order $q=p^r$ contains a subfield $K'$ of order $q'=p^k$ if and only if $k\mid r$.

$f:\mathbb{R}\to\mathbb{R}$ satisfies $f(3x)=3f(x)-4f(x)^3, \forall x\in\mathbb{R}$ and is continuous at $x=0$. Show that $|f(x)|\le 1, \forall x.$

Prove that $\frac{1}{\sqrt{1-x^2}}$ is unbounded for $x\in(-1,1)$

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