Question

A Banach space has an absolutely convergent basis $\iff$ it is topologically isomorphic to $\ell^1$

score 170 · Answer 1 · 2026-03-25 08:12:53

170

Views

A Banach space has an absolutely convergent basis $\iff$ it is topologically isomorphic to $\ell^1$

Published on 25 Mar 2026 - 8:12

score 415 · Answer 2 · 2016-12-23 23:24:40

415

Views

Alternative methods for finding antiderivative of $\frac x{(1+\sin x)^2}$

Published on 23 Dec 2016 - 23:24

score 1.1k · Answer 3 · 2026-04-01 19:16:02

1.1k

Views

Alternative proof and hints for: "rationals are dense in the reals" from Rudin's real analysis book

Published on 01 Apr 2026 - 19:16

score 915 · Answer 4 · 2016-12-25 08:55:25

915

Views

Is the set of rational numbers of absolute value $\geq 1$ together with $0$ a group under addition?

Published on 25 Dec 2016 - 8:55

score 135 · Answer 5 · 2016-12-28 05:33:47

135

Views

Let $(A, \star)$, and $(B, \diamond)$ be groups and let $A \times B$ be their direct product. Prove that $(1, 1)$ is the identity of $A \times B$

Published on 28 Dec 2016 - 5:33

score 80 · Answer 6 · 2016-12-28 23:27:15

80

Views

Arzelà-Ascoli on a sequence $\{f_n\}_{n\in\mathbb{N}}$ verifying $\int_{\mathbb{R}^2}f_n(\vec{x})^2+\|\nabla f_n(\vec x)\|^2d\vec x\le1$

Published on 28 Dec 2016 - 23:27

score 3k · Answer 7 · 2016-12-29 07:17:47

3k

Views

Given a quadrilateral, prove it is a square.

Published on 29 Dec 2016 - 7:17

score 205 · Answer 8 · 2016-12-30 00:18:33

205

Views

Prove that $\lim_{x\to0}\frac{\sin x}x=1$ using algebraic manipulations of derivatives?

Published on 30 Dec 2016 - 0:18

score 129 · Answer 9 · 2016-12-30 05:54:32

129

Views

If $\mathcal{T}$ is a topology and $B$ is a basis, does $\mathcal{T_1} \subset \mathcal{T_2} \implies \mathcal{B_1} \subset \mathcal{B_2}$?

Published on 30 Dec 2016 - 5:54

score 70 · Answer 10 · 2016-12-30 06:38:56

70

Views

Let $A$ be a finite set. If $X \subseteq A$, then $X$ is finite.

Published on 30 Dec 2016 - 6:38

score 244 · Answer 11 · 2026-03-27 13:47:25

244

Views

Isolated singularities of holomorphic function $f$ with $\mathfrak{R} f \geq 0$ are removable

Published on 27 Mar 2026 - 13:47

score 1.9k · Answer 12 · 2016-12-31 11:14:37

1.9k

Views

A simpler proof of $(1-x)^n<\frac{1}{1+nx}$

Published on 31 Dec 2016 - 11:14

score 145 · Answer 13 · 2017-01-02 15:56:53

145

Views

Prove that $\ln(x+\sqrt{x^2 + 4}) - \ln2$ is odd

Published on 02 Jan 2017 - 15:56

score 191 · Answer 14 · 2017-01-05 23:21:12

191

Views

Make this visual derivative of sine more rigorous

Published on 05 Jan 2017 - 23:21

score 75 · Answer 15 · 2017-01-06 01:41:20

75

Views

Why do I have to solve for $x$ in this proof, if I choose not to find a counterexample?

Published on 06 Jan 2017 - 1:41

List Question

A Banach space has an absolutely convergent basis $\iff$ it is topologically isomorphic to $\ell^1$

Alternative methods for finding antiderivative of $\frac x{(1+\sin x)^2}$

Alternative proof and hints for: "rationals are dense in the reals" from Rudin's real analysis book

Is the set of rational numbers of absolute value $\geq 1$ together with $0$ a group under addition?

Let $(A, \star)$, and $(B, \diamond)$ be groups and let $A \times B$ be their direct product. Prove that $(1, 1)$ is the identity of $A \times B$

Arzelà-Ascoli on a sequence $\{f_n\}_{n\in\mathbb{N}}$ verifying $\int_{\mathbb{R}^2}f_n(\vec{x})^2+\|\nabla f_n(\vec x)\|^2d\vec x\le1$

Given a quadrilateral, prove it is a square.

Prove that $\lim_{x\to0}\frac{\sin x}x=1$ using algebraic manipulations of derivatives?

If $\mathcal{T}$ is a topology and $B$ is a basis, does $\mathcal{T_1} \subset \mathcal{T_2} \implies \mathcal{B_1} \subset \mathcal{B_2}$?

Let $A$ be a finite set. If $X \subseteq A$, then $X$ is finite.

Isolated singularities of holomorphic function $f$ with $\mathfrak{R} f \geq 0$ are removable

A simpler proof of $(1-x)^n<\frac{1}{1+nx}$

Prove that $\ln(x+\sqrt{x^2 + 4}) - \ln2$ is odd

Make this visual derivative of sine more rigorous

Why do I have to solve for $x$ in this proof, if I choose not to find a counterexample?

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