Question

$f,f_n \in C[-1,1]$, $f_n \rightrightarrows f \implies \lim_{n \to \infty} \Vert f_n-f \Vert_{1} = 0$

score 39 · Answer 1 · 2026-03-29 14:59:23

39

Views

$f,f_n \in C[-1,1]$, $f_n \rightrightarrows f \implies \lim_{n \to \infty} \Vert f_n-f \Vert_{1} = 0$

Published on 29 Mar 2026 - 14:59

score 98 · Answer 2 · 2026-03-27 09:48:11

98

Views

Property of multiplication in (Banach) algebra $\ell^{1}(\mathbb{Z})$.

Published on 27 Mar 2026 - 9:48

score 88 · Answer 3 · 2019-12-03 11:23:47

88

Views

How to solve $y''(t) + 4 y (t) = 2t \cos (2t)$ on time in the exam?

Published on 03 Dec 2019 - 11:23

score 140 · Answer 4 · 2019-12-04 19:40:27

140

Views

$ \pi(n) > \frac{n}{22 \ln(n)} $ simple proof?

Published on 04 Dec 2019 - 19:40

score 80 · Answer 5 · 2026-03-28 15:21:17

80

Views

Proof of $f(x) = \sum_{k=0}^\infty a_kx^k$ with $a_0 := a_1 := 1$ and $a_{n+2} := a_n+a_{n+1}$

Published on 28 Mar 2026 - 15:21

score 477 · Answer 6 · 2019-12-04 20:59:32

477

Views

Proof $\frac{1}{f_n}$ converges uniformly towards $\frac{1}{f}$

Published on 04 Dec 2019 - 20:59

score 50 · Answer 7 · 2026-03-29 16:03:09

50

Views

Let $X=Y=[0,1]$ and $g(x, y)=\max \{x(1-2 y), y(1-2 x)\}$. How to compute $\max_{x \in X} \min_{y \in Y} g(x,y)$?

Published on 29 Mar 2026 - 16:03

score 200 · Answer 8 · 2019-12-05 16:50:57

200

Views

Alternative metric space proof for $d(x,y)\geq 0$

Published on 05 Dec 2019 - 16:50

score 1.2k · Answer 9 · 2019-12-07 20:18:36

1.2k

Views

Using Fermat's Little Theorem to Show Divisibility

Published on 07 Dec 2019 - 20:18

score 85 · Answer 10 · 2019-12-08 11:39:00

85

Views

Prove that $\lim_{n \to\infty}(1+\frac{1}{n})^n =\lim_{n \to\infty} (\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\dots + \frac{1}{n!})$

Published on 08 Dec 2019 - 11:39

score 194 · Answer 11 · 2026-03-25 17:25:02

194

Views

Another proof for complex solutions and solutions in finite fields

Published on 25 Mar 2026 - 17:25

score 50 · Answer 12 · 2019-12-12 14:00:43

50

Views

Angle between two lines without using the tan identity

Published on 12 Dec 2019 - 14:00

score 54 · Answer 13 · 2026-03-25 17:26:07

54

Views

Alternative proof sketch of Bertrand's Postulate from GCD

Published on 25 Mar 2026 - 17:26

score 1.9k · Answer 14 · 2026-03-25 17:24:48

1.9k

Views

A trivial proof of Bertrand's postulate

Published on 25 Mar 2026 - 17:24

score 350 · Answer 15 · 2019-12-14 22:20:06

350

Views

How to prove that $e^x +1- \sin(x) > 0$?

Published on 14 Dec 2019 - 22:20

List Question

$f,f_n \in C[-1,1]$, $f_n \rightrightarrows f \implies \lim_{n \to \infty} \Vert f_n-f \Vert_{1} = 0$

Property of multiplication in (Banach) algebra $\ell^{1}(\mathbb{Z})$.

How to solve $y''(t) + 4 y (t) = 2t \cos (2t)$ on time in the exam?

$ \pi(n) > \frac{n}{22 \ln(n)} $ simple proof?

Proof of $f(x) = \sum_{k=0}^\infty a_kx^k$ with $a_0 := a_1 := 1$ and $a_{n+2} := a_n+a_{n+1}$

Proof $\frac{1}{f_n}$ converges uniformly towards $\frac{1}{f}$

Let $X=Y=[0,1]$ and $g(x, y)=\max \{x(1-2 y), y(1-2 x)\}$. How to compute $\max_{x \in X} \min_{y \in Y} g(x,y)$?

Alternative metric space proof for $d(x,y)\geq 0$

Using Fermat's Little Theorem to Show Divisibility

Prove that $\lim_{n \to\infty}(1+\frac{1}{n})^n =\lim_{n \to\infty} (\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\dots + \frac{1}{n!})$

Another proof for complex solutions and solutions in finite fields

Angle between two lines without using the tan identity

Alternative proof sketch of Bertrand's Postulate from GCD

A trivial proof of Bertrand's postulate

How to prove that $e^x +1- \sin(x) > 0$?

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