Question

Showing $\mathbb{Q} \cap [a,b]$ is an open set in $\mathbb{Q}$ for irrational $a$, $b$.

score 452 · Answer 1 · 2026-04-16 07:11:39

452

Views

Showing $\mathbb{Q} \cap [a,b]$ is an open set in $\mathbb{Q}$ for irrational $a$, $b$.

Published on 16 Apr 2026 - 7:11

score 438 · Answer 2 · 2026-04-14 13:15:13

438

Views

How to evaluate $\int \frac{x^3}{\sqrt {x^2+1}}dx$

Published on 14 Apr 2026 - 13:15

score 104 · Answer 3 · 2026-04-28 16:32:21

104

Views

Can any improvements be made to my proof that "$\sqrt{3} $ is irrational"?

Published on 28 Apr 2026 - 16:32

score 324 · Answer 4 · 2026-04-13 05:11:48

324

Views

Calculating the derivative of a one-dimensional ODE

Published on 13 Apr 2026 - 5:11

score 211 · Answer 5 · 2026-04-09 06:21:15

211

Views

An extension of a corollary of the Arzela-Ascoli theorem for smooth functions

Published on 09 Apr 2026 - 6:21

score 51 · Answer 6 · 2026-04-16 17:24:33

51

Views

Find good substitution for PDE.

Published on 16 Apr 2026 - 17:24

score 1.3k · Answer 7 · 2026-04-11 23:06:52

1.3k

Views

Injective linear transformation and linearly independent vectors

Published on 11 Apr 2026 - 23:06

score 106 · Answer 8 · 2026-04-14 18:30:05

106

Views

Do these arguments correctly predict $\sum_{r=1}^n \mu(r)$

Published on 14 Apr 2026 - 18:30

score 2.2k · Answer 9 · 2026-04-15 11:46:44

2.2k

Views

Given Markov chain transition matrix, calculate $\mathbb{P}(X_1=3|X_2=1).$

Published on 15 Apr 2026 - 11:46

score 36 · Answer 10 · 2026-04-10 20:24:20

36

Views

Show $\Delta(\theta)\mathbb{Z} = \Delta(R/\mathbb{Z}) \implies R = \mathbb{Z}[\theta]$.

Published on 10 Apr 2026 - 20:24

score 63 · Answer 11 · 2026-04-15 06:53:14

63

Views

$R$ commutative ring with with unity. Then: "$(x)$ prime $\iff R$ domain" and "$(x)$ maximal $\iff R$ is a field."

Published on 15 Apr 2026 - 6:53

score 87 · Answer 12 · 2026-04-15 19:34:59

87

Views

number of ways to arrange 11 presents

Published on 15 Apr 2026 - 19:34

score 102 · Answer 13 · 2026-04-12 13:25:57

102

Views

Is my proof correct???

Published on 12 Apr 2026 - 13:25

score 90 · Answer 14 · 2026-04-12 03:16:35

90

Views

What is wrong with this argument? $R/I \approx R$

Published on 12 Apr 2026 - 3:16

score 1.3k · Answer 15 · 2026-04-28 16:32:21

1.3k

Views

Show that a function $f: A \to B$ is surjective if and only if it has a right inverse.

Published on 28 Apr 2026 - 16:32

List Question

Showing $\mathbb{Q} \cap [a,b]$ is an open set in $\mathbb{Q}$ for irrational $a$, $b$.

How to evaluate $\int \frac{x^3}{\sqrt {x^2+1}}dx$

Can any improvements be made to my proof that "$\sqrt{3} $ is irrational"?

Calculating the derivative of a one-dimensional ODE

An extension of a corollary of the Arzela-Ascoli theorem for smooth functions

Find good substitution for PDE.

Injective linear transformation and linearly independent vectors

Do these arguments correctly predict $\sum_{r=1}^n \mu(r)$

Given Markov chain transition matrix, calculate $\mathbb{P}(X_1=3|X_2=1).$

Show $\Delta(\theta)\mathbb{Z} = \Delta(R/\mathbb{Z}) \implies R = \mathbb{Z}[\theta]$.

$R$ commutative ring with with unity. Then: "$(x)$ prime $\iff R$ domain" and "$(x)$ maximal $\iff R$ is a field."

number of ways to arrange 11 presents

Is my proof correct???

What is wrong with this argument? $R/I \approx R$

Show that a function $f: A \to B$ is surjective if and only if it has a right inverse.

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