Question

If $\frac1\alpha+\frac1\beta=1$, irrational, then $\{\lfloor n\alpha\rfloor:n\in\Bbb N\}\uplus\{\lfloor n\beta\rfloor:n\in\Bbb N\}=\Bbb N$

score 691 · Answer 1 · 2026-03-26 23:10:37

691

Views

If $\frac1\alpha+\frac1\beta=1$, irrational, then $\{\lfloor n\alpha\rfloor:n\in\Bbb N\}\uplus\{\lfloor n\beta\rfloor:n\in\Bbb N\}=\Bbb N$

Published on 26 Mar 2026 - 23:10

score 2k · Answer 2 · 2026-03-26 16:06:30

2k

Views

Is there any geometry where ratio of circle's circumference to its diameter is rational?

Published on 26 Mar 2026 - 16:06

score 298 · Answer 3 · 2026-03-27 07:48:26

298

Views

Values $nx - [nx]$ are distinct for an irrational number

Published on 27 Mar 2026 - 7:48

score 1.3k · Answer 4 · 2026-03-25 21:47:33

1.3k

Views

2.71828. And then another 1828.

Published on 25 Mar 2026 - 21:47

score 290 · Answer 5 · 2014-04-22 22:01:09

290

Views

$\sqrt[3]{2}$ is not the root of a quadratic with rational coefficients?

Published on 22 Apr 2014 - 22:01

score 1.8k · Answer 6 · 2014-04-23 20:37:33

1.8k

Views

How can you proof that the sum of three roots is irrational?

Published on 23 Apr 2014 - 20:37

score 140 · Answer 7 · 2026-03-29 14:02:43

140

Views

Prove that if $y,z \in\Bbb Q$ then $y^z \in\Bbb A$

Published on 29 Mar 2026 - 14:02

score 4.1k · Answer 8 · 2026-03-29 14:25:12

4.1k

Views

Let $a,b \in R$ where $ a < b$. Prove that there exist a rational number $c$ and an irrational number $d$ such that $ a <c<b$ and $ a<d<b$.

Published on 29 Mar 2026 - 14:25

score 320 · Answer 9 · 2014-04-24 11:46:21

320

Views

Is $\ \Large\pi^e$ rational?

Published on 24 Apr 2014 - 11:46

score 288 · Answer 10 · 2026-03-25 21:53:30

288

Views

Question about $e^{e^{e^e}}$

Published on 25 Mar 2026 - 21:53

score 4.2k · Answer 11 · 2026-03-25 10:52:14

4.2k

Views

Irrational fractional parts - patterns

Published on 25 Mar 2026 - 10:52

score 1.6k · Answer 12 · 2026-03-29 14:00:56

1.6k

Views

Is the Nested Radical Constant rational or irrational?

Published on 29 Mar 2026 - 14:00

score 187 · Answer 13 · 2014-05-01 18:52:28

187

Views

Cantor's proof on uncountability of irrationals

Published on 01 May 2014 - 18:52

score 1k · Answer 14 · 2014-05-02 18:29:34

1k

Views

Prove the irrationality of $0.235711131719...$

Published on 02 May 2014 - 18:29

score 90 · Answer 15 · 2014-05-04 07:27:15

90

Views

How to prove that: $\sqrt{25!+3} \in \mathbb{R}\setminus\mathbb{Q}$

Published on 04 May 2014 - 7:27

List Question

If $\frac1\alpha+\frac1\beta=1$, irrational, then $\{\lfloor n\alpha\rfloor:n\in\Bbb N\}\uplus\{\lfloor n\beta\rfloor:n\in\Bbb N\}=\Bbb N$

Is there any geometry where ratio of circle's circumference to its diameter is rational?

Values $nx - [nx]$ are distinct for an irrational number

2.71828. And then another 1828.

$\sqrt[3]{2}$ is not the root of a quadratic with rational coefficients?

How can you proof that the sum of three roots is irrational?

Prove that if $y,z \in\Bbb Q$ then $y^z \in\Bbb A$

Let $a,b \in R$ where $ a < b$. Prove that there exist a rational number $c$ and an irrational number $d$ such that $ a <c<b$ and $ a<d<b$.

Is $\ \Large\pi^e$ rational?

Question about $e^{e^{e^e}}$

Irrational fractional parts - patterns

Is the Nested Radical Constant rational or irrational?

Cantor's proof on uncountability of irrationals

Prove the irrationality of $0.235711131719...$

How to prove that: $\sqrt{25!+3} \in \mathbb{R}\setminus\mathbb{Q}$

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